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CONTENTS 

SEC.  PAGE 

1  Introduction.    Purpose.     Problem.    Previous  Investigation . .  i 

2  Limitations 5 

3  The  Original-List - 6 

4  The  Selected  List.     1 8-Word  List t ..  8 

5  The  Preferred  Lists ii 

6  Examination  of  the  First  Preferred  List i6 

7  Examination  of  the  Second  Preferred  List , 22 

8  Conclusions  Regarding  the  Preferred  Lists 25 

9  Ratings  of  Individual  Pupils 27 

I  o     Overlapping 31 

I I  Location  of  Grade  Medians 34 

1 2  Scaling  the  Words 40 

1 3  The  Use  of  the  Scale 51 

14  The  Zero-Point  of  Spelling  Ability 55 

15  Observations  on  the  Distributions  shown  in  Fig.  21 61 

16  Supplementary  Testing  at  Schools  VI  and  VII 65 

17  Arrangement  of  the  Words  of  the  Preferred  List  by  Teach- 

ers' Judgments ^ .  69 

18  Rice  Sentence  Test.     Easy  50-Word  Test 75 

1 9  Derived  Forms  of  Distribution 84 

20  Conclusions no 

Appendix 113 


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3  822  02683  2881 


INDEX  OF  TABLES 

NO.  PAGE 

I     Sample  of  word-ratings  from  Original  (270)  Word  List. 

Schools  I  and  II 8 

II     Sample   of   word-ratings    (118   words)   30-86.     Schools 

III,  IV,  and  V 12 

III  Number  correct,   per  cent   correct,  and  rank  of   each 

word,  First  Preferred  List 14 

IV  Number   correct,    per  cent   correct,  and  rank  of   each 

word,  Second  Preferred  List 15 

V    Table  to  show  method  of  deriving  r- values  by  "foot- 
rule  "  method 18 

VI     r-values  between  grades  of  School  I  (3  methods) 19 

VII     Coefficients  of  Correlation,  grade  with  grade,  and  each 
grade  with  all  grades  for  each  school   (II,    III,    IV 

and  V).     First  Preferred  List 20 

VIII     Correlations  of  school  with  school  and  of  each    school 

with  all  schools  for  each  grade.     First  Preferred  List     21 
IX     Coefficients  of  Correlation,  grade  with  grade  and  each 
grade  with  all  grades  for  each  school.     Second  Pre- 
ferred List 23 

X     Correlations  of  school  with  school  and  of  each  school 
with  all  schools  for  each  grade.      Second   Preferred 

List 24 

XI     Distribution  of  individual  ratings  of  pupils  in  Schools 

II,  III,  IV,  and  V 27 

XII     Distribution    of    individual    ratings    grouped    to   show 

modes 28 

XIII  Number  and  per  cent  of  pupils  in  each  grade  whose 

ability  equaled  or  exceeded  that  of  the  median  pupil 

in  every  other  grade 32 

XIV  Table   of   values   of   the   Normal   Probability   Integral 

corresponding  to  values  of  P.E 35 

XV     The   per  cent   of  pupils   in  each  grade   whose   ability 
equaled   or   exceeded   that   of   the   median    pupil   in 
every  other  grade  with  corresponding  P.E.  values.  .      36 
XVI     Direct  and  derived  values  of  median  distances  in  terms 

of  P.E 39 

XVII     Per    cents    and    P.E.    equivalents.    Preferred    List — all 

grades 45 

XVIII     Grade  positions  and  average  positions 48 

XIX     Words    arranged    in    order    of    difficulty    according    to 
scale,  their  P.E.  values  and  weights  on  a  per  cent 

basis 51 

XX     A  ten-point  scale 52 

XXI     Distribution  of  individual  ratings.     Easy  50-Word  Test     57 

V 


VI 


Index  of  Tables 


NO.     '  PAGE 

XXII     Amount  and  per  cent  of  overlapping  with  P.E.  equiva- 
lents.    Easy  50-Word  Test 58 

XXIII  Values  of  median  intervals  and  their  derivation  (2a  to 

4th  grade) 59 

XXIV  Median  Intervals  o-8th  grade 61 

XXV    Distribution  of  individual  ratings,  Schools  VI  and  VII. 

Selected  List 66 

XXVI     Comparison  of  results  obtained  in  Schools  VI  and  VII 

with  those  in  Schools  II,  III,  IV,  and  V 66 

XXVII  Number  and  per  cent  of  pupils  in  each  grade  who 
equalled  or  exceeded  the  median  of  every  other  grade 
with  P.E.'s.       Schools  VI  and  VII  combined  with  II, 

III,  IV,  and  V 68 

XXVIII     Median  Distances  derived  from  Table  XXVII 69 

XXIX     Comparison   of   results   by    Record   and   by   Teachers' 

Judgments.     Preferred  List 72 

XXX     Distribution  of  individual  ratings.     R.  S.  T 76 

XXXI     Per  cent  correct  for  each  word  in  each  grade  with  P.E. 

values.     R.  S.  T 78 

XXXII     Per  cent  correct  for  each  word  in  each  grade  with  P.E. 

values.     Easy  50-Word  Test 80 

XXXIII  Percentages  of  Retention — Grades  3-8 87 

XXXIV  Plan  of  elimination  and  retention  for  each  grade 89 

XXXV     Derivation  of  6th-grade  Modified  Table  of  Frequency .  .      92 

XXXVI     Modified  Table  of  Frequency,  3d  grade 93 

XXXVII     Modified  Table  of  Frequency,  4th  grade 94 

XXXVIII     Modified  Table  of  Frequency,  5th  grade 95 

XXXIX    Modified  Table  of  Frequency,  6th  grade 96 

XL    Modified  Table  of  Frequency,  7th  grade 97 

XLI     Modified  Table  of  Frequency,  8th  grade 98 

XLII  Number  and  per  cent  of  pupils  in  each  grade  whose 
ability  equalled  or  exceeded  that  of  the  median  pupil 
in  every  other  grade  with  the  P.E.  values  corres- 
ponding to  each  per  cent.  Modified  Distributions  ...  10 1 
XLIII  Direct  and  derived  values  of  Median  Distances.  Modi- 
fied Distributions 102 

XLIV    Comparison  of  Average  Median  Distances  by  Normal 

and  Modified  Distributions 103 

XLV     Per  cent  correct  for  each  word  of  Preferred  List  with 
corresponding    P.E.   values  by  Normal  Distribution 

and  by  Modified  Distributions 104 

XLVI     Average  position  of  each  word  by  Normal  Distribution 
and  by  Modified  Distributions.     Point  of  reference, 

3d-grade  median 108 

XLVII     P.E.    values   corresponding  to    given  per  cents  of  the 

Normal  Surface  of  Frequency 116 


INDEX  OF  FIGURES 

NO.  PAGE 

1  Distribution  of  Individual  Ratings.    Selected  List,  3d  Grade  29 

2  Distribution  of  Individual  Ratings.  Selected  List,  4th  Grade  29 

3  Distribution  of  Individual  Ratings.  Selected  List,  5th  Grade  29 

4  Distribution  of  Individual  Ratings.  Selected  List,  6th  Grade  29 

5  Distribution  of  Individual  Ratings.  Selected  List,  7th  Grade  29 

6  Distribution  of  Individual  Ratings.  Selected  List,  8th  Grade  30 

7  Distribution  of  Individual  Ratings.  Selected  List,  All  Grades  30 

8  Distribution  of  Individual  Ratings.  Rice  Sentence  Test,  6th 

Grade 33 

9  Distribution  of  Individual  Ratings.    Rice  Sentence  Test,  7th 

Grade 33 

10  Distribution  of  Individual  Ratings.    Rice  Sentence  Test,  8th 

Grade 33 

11  Showing  the  Overlapping  of  the  3d  and  4th  Grade  Surfaces 

of  Frequency 34 

12  Normal  Frequency  Surface  to  Illustrate  Word  Placing 41 

13  Showing  the  Placing  of  the  first  seven  words  of  the  Pre- 

ferred List,  3d  Grade 43 

14  3d  Grade  Scale.     Preferred  List 44 

1 5  4th  Grade  Scale.     Preferred  List 44 

16  5th  Grade  Scale.     Preferred  List 44 

1 7  6th  Grade  Scale.     Preferred  List 44 

18  7th  Grade  Scale.     Preferred  List 44 

19  8th  Grade  Scale.     Preferred  List 44 

20  General  Scale,  Preferred  List 49 

21  Series  of  Grade  Distributions  (normal)  showing  Median  In- 

tervals  and   the   Zero-point.      Entire   range   of    Spelling 
AbiUty  in  the  Elementary  School 62 

22  Diagram  showing  difference  in  difficulty  between  words  by 

Teachers'  Judgments 73 

23  Distribution  of  Individual  Ratings.    Rice  Sentence  Test,  4th 

Grade 77 

24  Distribution  of  Individual  Ratings.    Rice  Sentence  Test,  sth 

Grade 77 

25  Scales  for  the  following  grades  and  lists: 

4th;  Preferred,  Rice  Sentence,  Easy  50-Word, 
5th;  Preferred,  Rice  Sentence, 


6th;  Preferred,  Rice  Sentence, 


7th;  Preferred,  Rice  Sentence,  .  ing 

p.  80 


8th;  Preferred,  Rice  Sentence. 

vii 


Fac- 


viii  Index  of  Figures 

NO.  PAGE 

26  2a  Grade  Scale,  Easy  50-Word;    26  Grade  Scale,  Easy  50-  ] 

Word I  Fac- 

27  3d  Grade  Scale;  Preferred  and  Easy  50-Word \  jng 

28  General  Scale;  (2a  to  4th  Grade  combined)  Easy  50- Word  1  p.  82 

29  General  Scale;  Preferred,  Rice  Sentence  Test,  Easy  50-Word  J 

30  Curves  of  Retention,  3d  to  8th  Grades 88 

31-36     The  amount  and  distribution  of  elimination  and  retention. 

Grades  3  to  8 9° 

37-42     Derived  Forms  of  Distribution.      Grades  3  to  8 99 

43-47     Comparison  of  Grade  scales  according  to  (a)  Normal  Dis- 
tribution and  (b)  Modified  Distributions 106-107 

48     Comparison  of  General  scales  according  to  (a)  Normal  Dis- 
tribution and  (b)  Modified  Distributions 109 


SPELLING  ABILITY— ITS  MEASUREMENT  AND 
DISTRIBUTION 

§   I.     Introduction 

The  purpose  of  this  dissertation  is  to  derive  a  scale  for  the 
measurement  of  spelling  ability  and  to  show  some  of  its  uses 
and  applications.  Such  a  purpose  relates  itself  closely  to  a 
general  movement,  which  is  now  well  under  way,  and  which 
aims  to  place  in  our  hands  the  means  of  stating  with  some- 
thing approaching  the  precision  of  objective  measurement  the 
amounts  of  each  school  ability  possessed  by  an  individual  or 
a  group.  We  received  not  long  ago  a  scale  for  Handwriting 
(Thorndike,  E.  L.,  1910)  and  still  more  recently  a  scale  for 
English  Composition  (Hillegas,  Milo  B.,  1912).  The  former 
consists  in  the  use  of  selected  specimens  of  handwriting  each 
of  which  has  been  evaluated ;  the  latter  consists  of  a  similar 
series  of  English  compositions.  It  will  be  noticed  that  some 
of  the  conditions  of  objective  measurement  are  met.  We  meas- 
ure given  specimens  of  handwriting  by  comparing  them  with 
actual  samples  of  handwriting  of  known  value.  We  determine 
the  quality  of  English  composition  by  a  like  comparison  with 
samples  of  actual  English  writing  of  known  value. 

It  seems  clear,  therefore,  that  if  we  are  to  measure  ability 
in  spelling  at  all  it  will  be  by  reference  to  an  evaluated  standard 
or  sample  of  spelling.  If  we  can  arrange  a  series  of  words  on 
a  linear  projection  in  such  a  way  that  the  words  from  the  low 
end  to  the  high  end  are  placed  at  equal  intervals  determined 
by  the  difficulty  of  each  word,  and  if  we  can  determine  a 
zero-point  such  that  failure  to  spell  the  word  fixed  at  that  point 
under  the  required  conditions  indicates  absence  of  spelling  abil- 
ity, then  we  shall  have  constructed  a  scale  by  which  we  may 
measure  the  spelling  ability  of  an  individual,  or  by  which  we 
may  through  suitable  tests  determine  the  difficulty  of  any 
word  in  the  language.     Since  the  spelling  of  individuals  may 

I 


2         Spelling  Ability — Its  Measurement  and  Distribution 

thus  be  rated,  the  spelling  of  classes,  of  schools,  and  of  school 
systems  may  likewise  be  rated. 

It  may  be  said  that  we  have  always  rated  pupils  in  spelling; 
and  that  schools  and  school  systems  have  likewise  been  rated. 
Such  is  indeed  the  case.  But  there  has  always  been  a  lack  of 
precision  in  these  ratings  due  to  the  inequality  of  the  units  em- 
ployed. Dr.  Rice  (Rice,  '97),  for  example,  in  testing  the  pupils 
in  4th  to  8th  grades  in  twenty-one  school  systems  used  a  list 
of  words  containing  among  others:  disappoint,  necessary, 
changeable,  better,  because,  picture.  The  method  of  rating 
pupils  was  the  usual  one  of  deducting  from  100  per  cent  the 
same  per  cent  for  each  word.  That  is,  all  words  were  taken  as 
equal  measures  of  spelling  ability.  A  moment's  attention  to  the 
six  words  mentioned  will  lead  us  to  suspect  that  this  is  not  a  true 
assumption ;  and  an  actual  test  of  a  group  of  5th-year  children 
with  these  words  shows  that  our  suspicion  is  correct.  In  such 
a  test  mistakes  were  made  as  follows : 

disappoint,  37 

necessary,  42 

changeable,  42 

better,  3 

because,  i 

picture,  o  (Thorndike,  '04,  p.  8) 

To  give  these  words  equal  weight  in  any  test  is  to  make 
inaccurate  most  of  the  conclusions  based  upon  it.  A  pupil  who 
spells  all  or  nearly  all  of  the  list  is  a  much  better  speller  than 
the  figures  show ;  for  he  has  probably  spelled  not  only  all  the 
easy  words  but  also  many  of  the  hard  ones.  On  the  other  hand, 
a  pupil  who  misses  most  of  the  words  is  a  much  poorer  speller 
than  his  rating  indicates  because  he  has  probably  failed  to  spell 
all  the  hard  words  as  well  as  most  of  the  easy  ones. 

Nor  is  this  list  of  Dr.  Rice's  at  all  unusual.  Comman  used 
the  same  list  (Comman,  '02).  Both  used  a  composition  test 
where  pupils  were  rated  according  to  the  per  cent  of  their 
correctly  spelled  words  among  the  total  number  of  words  in  a 
written  exercise.     Cornman  also  used  a  test  in  which  school 


Introduction  3 

children  were  required  to  write  "  as  many  words  as  they  could  " 
in  15  minutes.  Of  course  in  the  composition  test  and  in  the 
15-minute  test  no  two  children  wrote  the  same  words.  More- 
over, the  words  written  by  each  child  must  have  varied  widely 
in  difficulty.  The  result  for  the  15-minute  test,  according  to 
Comman's  best  table,  is  as  follows: 


School  Year 

Median  Percentage 

Average  Variation 

8th 

97.9 

.60 

7th 

96.2 

.50 

6th 

95.2 

.33 

5tha 

94.3 

.36 

5th& 

94.3 

.10 

4tha 

94.7 

.66 

4th6 

93.7 

.96 

3da 

93.5 

.23 

3d6 

93.0 

1.43 

One  conclusion  from  this  is  that  "  pupils  of  the  elementary 
school  increase  regularly  from  grade  to  grade  in  accuracy  of 
spelling."  This  might  almost  be  taken  for  granted.  But  in 
answer  to  the  question,  "  How  much  does  one  grade  surpass 
another?"  the  figures  afford  no  information.  Obviously  from 
all  we  know  of  the  elementary  school,  the  difference  between 
eighth-grade  ability  and  low  third-grade  ability  in  spelling  is  far 
greater  than  the  figures  97.9  and  93  indicate. 

Similarly  the  Composition  Tests  of  Rice  and  Cornman  are 
misleading  when  used  to  indicate  spelling  ability.  According  to 
the  series  of  Composition  Tests  of  the  latter,  8th-year  children 
on  the  average  spelled  99.5  per  cent  of  their  words  correctly, 
and  children  of  the  first  half  of  the  3d  year  spelled  93.2  per  cent 
correctly.  The  author  draws  conclusions  from  his  figures  as 
to  the  progress  of  each  grade  for  the  school  year,  as  to  the 
progress  of  the  school  and  as  to  the  effect  of  the  suspension 
of  instruction  in  spelling.  Since  in  the  series  of  eight  tests 
the  children  wrote  various  kinds  of  lessons — Geography ,  History, 
Science,  Language,  Composition — each  with  its  own  peculiar 
words,  and  since  each  pupil  used  his  own  individual  vocabulary, 
we  cannot  escape  the  conviction  that  while  these  figures  may 
be  suggestive  of  progress,  or  of  the  effect  of  change  in  method, 
or  of  grade  differences,  they  are  nothing  more  than  suggestive. 


4         Spelling  Ability — Its  Measurement  and  Distribution 

They  leave  unanswered  the  questions, — How  much  progress? 
How  large  an  effect?  How  great  a  difference?  As  we  grow 
more  and  more  accustomed  to  quantitative  thinking  in  our  edu- 
cational work,  we  feel  that  these  are  precisely  the  questions  that 
we  ought  in  some  way  to  be  able  to  answer. 

These  studies  of  spelling  made  by  Comman  and  Rice  remain 
the  most  important  statistical  treatment  of  the  subject.  That 
they  have  not  great  value  it  would  be  presumptuous  even  to 
imply.  Their  results  are  in  a  general  sense  true.  To  a  certain 
extent  their  lists,  even  though  made  up  of  words  of  various 
and  undetermined  difficulty,  may  be  used,  especially  for  com- 
parative purposes,  as  a  total  measuring  device.  They  do,  how- 
ever, undoubtedly  suffer  through  lack  of  precision,  while  their 
statements  of  amounts  of  difference  are  in  general  misleading. 

The  same  thing  may  be  said  of  later  investigations.  For 
example,  Wallin's  tables  and  his  conclusions  from  them  as  to 
the  transfer  of  spelling  efficiency  and  its  relation  to  age,  grade, 
and  sex  are  subject  to  the  same  limitations  (Wallin,  'ii).  Pear- 
son's "  Experimental  Studies  in  the  Teaching  of  Spelling " 
(Pearson,  '12),  however,  shows  a  recognition  of  the  difficulty, 
although  it  offers  no  remedy.  In  his  treatment  of  the  relative 
values  of  the  "  together-method  "  and  the  "  separate-method  " 
of  teaching  homonyms  this  author  says :  "  Owing  to  the  in- 
equality of  the  units  of  measurements,  it  is  impossible  to  deter- 
mine accurately  from  Table  IV  whether  the  together-method 
is  superior  to  the  separate-method.  One  cannot  decide,  for 
example,  positively  whether  an  improvement  from  3.78  errors 
(median  of  a  class)  to  2.86  errors  is  greater  or  less  than  an 
improvement  from  5.6  errors  to  3.3  errors."  If,  however,  the 
words  used  could  have  been  evaluated  through  an  independent 
test  by  reference  to  a  scientifically  constructed  scale,  the  "  in- 
equality of  the  units  of  measurement "  would  have  disappeared. 
The  further  treatment  of  the  foreshortening  of  the  opportunity 
for  improvement  due  to  high  initial  performance  is  quite  another 
matter. 

It  will  be  clearly  seen  from  the  foregoing  that  in  practically 
all  work  which  has  attempted  to  present  the  spelling  situation 
statistically  it  is  assumed  as  fundamental  that  one  error  equals 


Limitations  5 

another  and  that  to  spell  one  word  is  the  same  as   to   spell 
another   word. 

It  will  therefore  be  profitable  to  seek  in  this  field  as  others 
have  sought  in  other  fields  to  devise  an  instrument  which  will 
more  accurately  measure  that  of  which  we  are  so  often  called 
upon  to  give  a  quantitative  statement. 

§  2.    Limitations 

The  study  here  attempted  is  confined  to  the  elementary  school 
entirely.  It  covers  the  grades  from  the  third  to  the  eighth,  both 
inclusive.  The  schools  tested  are  all  located  in  or  near  New 
York  City.  The  cosmopolitan  character  of  the  population  of 
the  metropolitan  area  makes  it  extremely  unlikely  that  results 
of  a  materially  different  character  would  have  been  obtained 
by  testing  schools  in  various  sections  of  the  country. 

It  is  believed  that  these  schools  are  fairly  typical  within  the 
limits  of  the  area  chosen.  School  I  is  a  private  school  of  high 
class  whose  pupils  are  mostly  American  born  and  from  good 
homes.  All  the  other  schools  are  public  schools.  School  II 
is  in  a  German  section  of  rather  low  class.  School  III  is  in  a 
better  neighborhood,  foreigners  predominating.  School  IV  is 
in  an  Italian  section.  It  has  long  had  the  benefit  of  high-class 
supervision  and  organization.  School  V  is  again  predominantly 
American.  It  is  located  outside  of  the  city  system.  School  VI 
is  in  a  good  residential  section  of  the  city.  School  VII  is  a 
large  school,  most  of  whose  pupils  are  of  foreign  parentage. 
Territorially,  two  schools  are  in  Manhattan,  one  in  the  Bronx, 
one  in  Brooklyn,  and  two  in  Queens,  while  one  is  outside  of  the 
city  entirely. 

In  all  8,791  pupils  were  tested.  It  is  thought  that  this  is  a 
sufficient  number  for  practical  purposes.  In  fact  it  was  found 
that  the  returns  from  each  additional  school  after  the  first  three 
or  four  made  almost  no  change  in  the  results.  It  is  probable 
that  greatly  increasing  the  number  of  pupils  tested  would  have 
afforded  little  compensation  for  the  additional  labor.  It  has 
seemed  wiser  to  limit  the  number  to  a  moderate  one  and  to 
spend  considerable  effort  in  making  the  statistical  analysis  as 
complete  as  possible. 


6         Spelling  Ability — Its  Measurement  and  Distribution 

§  3.     The  Original  List 

The  preliminary  testing  was  made  with  a  list  of  270  words. 
It  will  be  called  "  The  Original  List."  It  was  itself  selected 
from  a  much  larger  list  of  graded  words  used  by  the  author 
of  this  dissertation  in  his  own  school,  the  same  having  been 
secured  by  taking  from  five  of  the  popular  Spelling  Books  now 
in  use  a  vocabulary  of  5,000  words  agreed  upon  by  two  or  more 
of  the  books.  The  principles  of  selection  for  these  270  words 
were:  (i)  that  all  of  them  should  be  sufficiently  common  to  be 
in  the  speaking  vocabulary  of  third-grade  children;  and  (2)  that 
the  spelling  difficulty  of  many  of  them  should  be  great  enough 
to  test  the  ability  of  eighth-grade  children.  As  a  matter  of  fact, 
the  selection  did  not  consist  of  270  words  at  first.  The  list  grew 
to  that  number  only  after  the  chosen  words  were  put  into  sen- 
tences. The  necessary  helping  words  then  swelled  the  total  to 
the  number  given. 

The  sentences  were  dictated  during  the  fall  term  of  1910  to 
schools  I  and  II.  They  were  given  to  grades  3  to  8  in  School 
II,  and  to  grades  4  to  7  in  School  I.  Their  dictation  consumed 
several  periods  for  every  class.    The  following  are  the  sentences : 

There  were  forty  birds  on  the  bridge.  Do  not  go  until  I  come. 
On  Wednesday  an  umbrella  was  found.  Whose  pencil  is  this? 
My  uncle  gave  me  a  banana.  The  butcher  gave  the  hungry  dog 
a  piece  of  meat.  My  answer  is  ninety.  For  a  nickel  I  bought 
an  orange,  a  peach,  and  a.  pear.  A  dollar  is  not  too  much  money 
for  so  beautiful  a  picture.  Learn  to  do  right  because  it  is  right. 
The  chicken  ran  across  the  road.  The  janitor  sweeps  every  Tues- 
day afternoon.  It  is  wrong  to  steal  even  a  penny.  It  would  be 
easy  to  watch  for  your  cousin  from  the  parlor  window.  It  is 
the  hour  for  recess.  Smoke  was  coming  out  of  their  chimney. 
One  summer  evening  my  neighbor  came  into  my  kitchen.  I  did 
not  know  he  was  coming  that  night.  To  whom  does  this  pair  of 
scissors  belong?  I  am  almost  sure  they  belong  to  the  tailor. 
The  doctor  thought  he  ought  to  go  at  once.  His  bicycle  was 
against  the  fence.  But  a  carriage  was  stopping  in  front  of  his 
office.  His  friend  was  already  beginning  to  speak  to  him.  He 
said  the  soldier  should  have  medicine  this  minute.  Pshaw,  there 
was  neither  a  monkey  nor  an  elephant  at  the  circus.     Get  some 


The  Original  List  7 

coffee,  sugar,  and  soap  at  the  grocery  store.  The  soldier  dropped 
his  sword  and  pistol.  Jack  had  a  whistle  and  nineteen  nails  in 
his  pocket.  The  pretty  fairy  had  a  jawcy  tongue.  One  rfay  in 
February  people  saw  a  sleigh  pass  through  the  avenue.  Shoes 
are  made  of  leather  and  a  /tY^/^  iVon.  A  w^^fe  from  to-day  there 
^//  be  a  dance.  Cut  up  a  tomato  and  an  om'on  together.  In  my 
garden  I  jAa//  rau^  cabbage  instead  of  &^^fj.  The  saucer  was 
round  like  a  circle.  Make  no  noise;  do  not  whisper  or  laugh. 
Nobody  should  be  without  a  handkerchief.  A  straight  line  has 
length  only.  We  shall  believe  the  fn<?/j.  We  have  another  piano 
at  our  school.  Is  it  frzi^  that  there  was  grease  on  the  towel? 
This  animal  has  a  /ar^^  mouth.  It  is  not  o//t'M  co/rf  enough  for 
the  oc^aw  to  freeze.  Guess  what  made  me  sneeze.  Choose  which 
one  of  the  pigeons  you  like.  Touch  the  button  with  your  thumb. 
The  American  Indian  had  corn  and  tobacco.  I  have  written  the 
whole  alphabet.  1  wear  a  number  thirteen  collar.  If  the  w^n 
quarrel,  telephone  me  or  j^wc?  a  telegram.  Our  arithmetic  lesson 
is  in  addition.  We  a/^o  subtract.  A  handfid  of  corn  was  a//  I 
had  for  supper.  What  is  the  ft//^  of  the  story?  Did  you  /t^ar 
the  thunder  last  night?  I  am  ^_vm^  up  my  shoe.  A  &ajm  of 
water  sat  on  the  ^a&/^.    That  sentence  has  twelve  words  in  it. 

Those  who  dictated  the  sentences  were  directed  to  read  them 
in  whole  or  in  part  as  many  times  as  seemed  necessary  to  secure 
their  complete  comprehension.  Pupils  were  therefore  not  re- 
quired to  retain  in  mind  a  long  series  of  words. 

In  rating  the  papers  only  the  words  printed  in  italics  were 
considered.  If  a  word  occurred  twice  it  was  regarded  only  the 
first  time  it  appeared.  Omitted  and  illegible  words  were  classed 
as  wrong.  All  the  papers  here  as  well  as  elsewhere  throughout 
this  study  were  rated  by  the  same  person.  They  were  rated 
from  two  points  of  view:  (i)  as  to  the  number  of  times  each 
word  was  correctly  spelled,  and  (2)  as  to  the  per  cent  of  the 
entire  number  of  words  each  pupil  spelled  correctly.  The  former 
point  of  view  is  the  only  one  to  which  attention  is  now  directed. 

Table  I  is  a  sampling  from  the  entire  270  words  as  given  to 
schools  I  and  II.  At  School  I  the  grammar-school  course  is 
completed  in  seven  years.  It  therefore  has  no  8th  grade.  As 
stated  above,  the  test  was  not  given  to  the  3d  grade  in  this  school. 


8         Spelling  Ability — Its  Measurement  and  Distribution 


TABLE  I 

Figures  Indicate  Per  Cent  Correct 

lable  reads: 

"across"  was  spelled  correctly  in  the  3d  grade  of  School  II 

by  17%  of  the 

pupils;   in  the  4th  grade  of  School  I  by  60%  of  the  pupils, 

and  of  School 

II  by  40%  of  the  pupils,  etc 

Grade 

3d 

4th 

5th 

6th 

7th 

8th 

School 

II 

I 

II 

I 

II 

I 

II 

I 

II 

II 

across 

17 

60 

40 

76 

58 

90 

79 

98 

87 

93 

addition 

2 

38 

26 

60 

28 

76 

45 

94 

76 

83 

almost 

16 

62 

41 

73 

65 

88 

75 

80 

81 

87 

alphabet 

25 

13 

1 

63 

12 

40 

46 

82 

43 

68 

arithmetic. .  .  . 

27 

89 

53 

100 

72 

96 

92 

100 

97 

98 

bridge 

29 

59 

42 

87 

52 

98 

85 

100 

94 

97 

button 

14 

50 

35 

70 

49 

77 

63 

84 

62 

83 

choose 

6 

25 

10 

37 

31 

62 

37 

67 

55 

65 

day 

97 

100 

98 

96 

100 

100 

99 

100 

100 

100 

guess 

6 

29 

17 

67 

30 

77 

50 

82 

66 

85 

handful 

36 

47 

33 

46 

19 

76 

33 

75 

63 

57 

pshaw 

1 

4 

6 

29 

6 

46 

5 

31 

31 

18 

tomato 

34 

83 

49 

67 

43 

74 

48 

79 

32 

38 

too 

0 
17 

10 

49 

3 
15 

17 

40 

4 
29 

26 

47 

7 
10 

63 

57 

22 

59 

27 

whose 

66 

§  4.     The  Selected  List 

On  the  basis  of  the  results  for  the  Original  List,  a  group  of 
100  words  was  chosen.  It  is  here  called  the  "  Selected  List." 
In  Table  I  are  shown  15  words  from  the  Original  List.  The 
word  "  across  "  is  typical  of  the  words  taken  for  the  Selected 
List.  Since  17  per  cent  of  the  3d-grade  children  spelled  it  cor- 
rectly, it  was  not  so  difficult  in  that  grade  as  to  offer  no  test 
of  ability.  It  showed  a  steady  increase  throughout  the  following 
grades  but  did  not  reach  so  high  a  figure  in  the  highest  grades 
as  to  prevent  its  being  a  test  of  ability  there.  "Almost "  and 
"  button  "  were  chosen  for  the  same  reason.  "Addition  "  was 
not  taken  because  it  was  too  hard  for  3d-graders.  Only  2  per 
cent  wrote  it  correctly.  So  small  a  number  as  two  in  a  hundred 
might  get  it  right  by  chance.  Practically,  therefore,  the  word 
is  a  zero  word  for  the  3d  grade ;  and  such  a  word  does  not  test 
ability.  There  may  be — and  in  a  given  grade  there  certainly 
would  be — wide  differences  in  spelling  ability,  but  such  a  word 


The  Selected  List  g 

will  not  show  them.  "Alphabet "  was  rejected  because  though 
high  in  the  3d  grade  it  was  very  low  in  the  4th,  suggesting  that 
in  School  II  it  was  a  word  that  the  children  had  recently  studied. 
"Arithmetic  "  was  not  taken  because  from  the  6th  grade  on  it 
offered  practically  no  difficulty.  As  in  the  case  of  a  word  rated 
at  zero  or  nearly  zero,  so  in  the  case  of  a  word  rated  at  100 
or  nearly  100,  there  is  no  test.  Good  spellers  and  poor  spellers 
so  far  as  the  particular  word  is  concerned  behave  exactly  alike. 
"  Bridge  "  was  not  taken  for  the  same  reason.  "  Choose  "  was 
too  hard  in  the  3d  grade.  "  Day  "  was  too  easy  everywhere. 
In  fact  "  day  "  is  a  type  of  word  such  that  we  may  almost  be 
warranted  in  saying  that  one  who  cannot  spell  it  has  no  spelling 
ability.  "  Guess  "  was  taken  because  although  it  is  very  seldom 
spelled  correctly  in  the  3d  grade,  its  form  is  so  peculiar  that  the 
few  who  did  write  it  correctly  probably  knew  how  to  spell  it, 
i.e.,  did  not  get  it  right  by  chance.  "  Handful  "  is  a  type  of 
word  taken  because  although  it  shows  no  regular  increase  from 
grade  to  grade  it  offers  a  real  test  for  every  grade.  The  later 
results  in  other  schools,  however,  showed  that  its  irregularity 
is  not  accidental  in  schools  I  and  II  but  is  a  peculiarity  of  the 
word  itself.  "  Pshaw  "  is  a  familiar  word  to  the  ear,  but  not 
to  the  eye.  Very  few  get  it  right  in  any  grade.  It  was  rejected. 
"  Tomato  "  is  curious.  On  the  whole  neither  school  does  any 
better  with  it  in  the  highest  than  in  the  lowest  grades.  It  was 
not  taken.  This  word  and  the  w^ord  "  handful  "  strongly  suggest 
the  need  of  a  greater  number  of  pupils  to  test.  The  word  "  too  " 
is  a  word  which  is  misspelled  with  astonishing  frequency.  The 
difficulty  is  not  so  much  one  of  spelling  as  of  confusion  with  the 
other  two  words  which  have  the  same  pronunciation.  It  was 
not  used  in  the  Selected  List  but  was  later  included  in  a  small 
supplementary  list  just  to  "  try  it  out."  "  Whose  "  was  taken 
although  it  shows  a  dip  in  the  5th  and  6th  grades.  Pupils  in 
these  grades  have  learned  the  use  of  the  apostrophe  and  their 
"  little  knowledge  "  proves  a  "  dangerous  thing  "  which  the  pupils 
of  the  earlier  grades  avoid. 

These  words — each  more  or  less  typical  in  its  way — show  how 
from  the  Original  List  of  270  a  better  Selected  List  of  100  was 
chosen.    Again  the  words  were  put  into  sentences,  as  follows : 


lo       spelling  Ability — Its  Measurement  and  Distribution 

Whose  answer  is  ninety?  If  the  janitor  sweeps,  he  will  raise 
a  dust.  You  ought  not  to  steal  even  a  penny.  Wait  until  the 
hour  for  recess  to  touch  the  button.  Smoke  was  coming  out  of 
f/ifir  chimney.  Every  afternoon  the  butcher  gave  the  hungry 
dog  a  /JzVc^  of  meat.  One  evening  sl  carriage  was  stopping  in 
/row?  of  my  kitchen.  I  w^ar  a  number  thirteen  collar.  Guess 
what  made  me  sneeze.  Send  me  a  />air  of  leather  shoes.  I  do 
not  know,  but  I  am  almost  sure  they  are  mine.  My  uncle  bought 
my  cousin  a  pretty  watch  for  /or^y  dollars.  The  soldier  dropped 
his  sword.  Jack  had  a  whistle  and  a/.?o  twelve  nails.  The  ocean 
does  not  o//£^«  freeze.  You  should  speak  to  people  whom  you 
meet.  It  takes  ow/y  a  minute  to  ^a.yj  through  the  gate  and  across 
the  roaJ.  Did  you  ever  /^^ar  a  /airy  laugh f  The  American 
Indian  had  a  saucer  without  a  cup.  Neither  a  /'^ar  «or  a  peach 
was  at  the  grocery  store  to-day.  Cut  up  a  whole  onion  with  a 
handful  of  beans.  My  /jiawo  lesson  was  ^a.yy.  The  animal  ran 
fn/o  the  road  and  straight  against  a  tree.  '  Give  me  another  sen- 
tence which  has  the  word  "title"  in  it.  I  believe  true  friends 
like  to  be  together  instead  of  apart. 

These  sentences  were  dictated  at  schools  III,  IV,  and  V  in 
the  spring  term  of  191 1.  They  were  later  (fall  of  1912)  dictated 
at  schools  VI  and  VII. 

The  following  instructions  were  given  to  the  examiners : 

Please  read  these  instructions  through  before  beginning  to  dic- 
tate the  sentences. 

I.  See  that  each  sheet  is  headed  with  (a)  the  pupil's  name, 
(b)  the  date,  (c)  the  grade,  (d)  the  name  of  the  school. 

II.  Give  all  the  sentences  during  one  session,  i.e.,  either  in 
the  morning  or  the  afternoon  of  the  same  day. 

III.  In  classes  below  the  fifth  year  dictate  in  two  periods, 
separated  by  at  least  half  an  hour,  or  by  a  recess  period. 

IV.  Each  sentence  may  be  dictated,  either  in  whole  or  in  part, 
as  many  times  as  may  seem  necessary  to  secure  its  complete 
understanding.  This  exercise  is  purely  a  test  in  spelling.  It  is 
not  intended  that  pupils  should  be  subjected  to  the  added  diffi- 
culty of  an  effort  to  recall  the  words  dictated. 

V.  Offer  no  explanation  of  words  or  sentences.  If  the  mean- 
ing is  not  clear,  repeat  the  sentence  as  a  whole  or  in  part. 

VI.  Do  not  ask  the  children  to  underline  words  nor  otherwise 
call  their  attention  to  the  significant  words  of  the  sentences. 


The  Preferred  Lists  ii 

VII.  After  the  children  have  written  the  sentences,  read  them 
again  and  allow  pupils  to  insert  words  or  make  other  corrections. 

VIII.  Collect  the  papers. 

Subsequently  at  the  same  schools  (III,  IV,  and  V)  was  given 
a  supplementary  list  of  i8  words,  again  selected  from  the 
Original  List  (270  words).  With  the  same  directions  to  the 
examiners,  these  words  were  put  into  sentences  as  follows : 

Telephone  me  on  Tuesday  if  the  tobacco  comes.  The  taiior 
sent  a  saucy  telegram.  Already  the  circus  was  beginning. 
Pigeons  seem  too  beautiful  to  quarrel.  I  am  trying  to  choose  a 
towel.    The  chicken  was  fried  in  grease. 

Each  of  these  118  words  was  scored  in  each  grade  and  for 
each  school  separately.  Table  II  illustrates  for  a  few  of  the 
words  the  manner  in  which  this  was  done.  The  figures  indicate 
per  cent  correct,  ^a  means  third  grade,  first  half ;  3&  third  grade, 
second  half,  etc.     Ill,  IV,  and  V  refer  to  different  schools. 

It  will  be  seen  at  once  that  there  is  no  steady  progression  for 
each  word  as  we  pass  from  the  lowest  to  the  highest  grades.  In 
fact  for  this  and  for  other  reasons  it  was  found  best  to  deal 
with  grades  by  years  rather  than  by  half-years.  It  also  seemed 
advisable  to  choose  a  few  of  these  words  and  to  make  them 
the  basis  of  study. 

§  5.  The  Preferred  Lists 
From  the  data  now  in  hand  it  was  possible  to  select  a  few 
words  which  showed  reasonably  regular  increase  from  grade  to 
grade  in  the  per  cent  of  times  they  were  spelled  correctly.  Two 
lists  were  made  up,  each  containing  twenty-five  words.  The 
first  list  is  superior  to  the  second  in  the  testing  power  of  the 
words  in  all  grades  and  in  the  permanence  of  their  relative  diffi- 
culty throughout  the  grades.  That  is,  to  a  somewhat  greater 
extent  than  in  the  case  of  the  second  list,  the  words  of  the  first 
list  are  found  to  be  easy  enough  for  low  grades  and  hard  enough 
for  high  grades.  Also,  a  word  occupying  a  certain  serial  posi- 
tion (say  the  4th  in  point  of  difficulty  for  the  third  grade)  tends 
more  strongly  in  the  first  than  in  the  second  list  to  occupy  the 
same  position  in  all  other  grades.  That  both  lists,  however,  are 
reasonably  satisfactory  in  these  particulars  will  be  abundantly 
shown. 


12       Spelling  Ability — Its  Measurement  and  Distribution 


TABLE  II 
Figures  Indicate  Per  Cent  Correct 


Grade  

3a 

3b 

4a 

46 

5a 

56 

6a 

66 

7a 

76 

8a 

86 

against 

III 

20 
5 
0 

8 
0 
0 

12 
10 
11 

22 
37 
33 

56 

15 

0 

0 
8 
0 

7 

10 

0 

0 
3 
0 

60 

19 

0 

77 
3 
4 

16 
39 

28 

40 
61 
38 

61 
25 
11 

2 
6 

45 

4 
10 
16 

0 
45 
45 

54 
26 
10 

37 
17 
24 

44 
38 
45 

63 
68 
62 

65 
54 

28 

13 

74 
9 

17 
16 
31 

15 

34 

0 

43 
29 
15 

54 
36 
14 

72 

58 
38 

75 
71 
60 

46 
19 
14 

31 
50 
32 

52 
36 
19 

58 
27 
85 

60 
70 
30 

53 

32 

28 

78 
72 
55 

73 
78 
60 

60 
59 
36 

24 
63 
61 

45 
49 
21 

64 
54 

18 

62 
61 
52 

44 
22 
55 

83 
82 
68 

70 
81 
84 

65 
49 
52 

61 
22 
50 

40 
51 
52 

46 
40 
26 

60 
92 
54 

35 
50 
76 

91 
97 

84 

88 
85 
80 

70 
61 
64 

66 
57 

82 

33 
73 
66 

14 
10 
36 

91 

78 
74 

57 
52 
50 

95 
93 

74 

82 
93 
79 

86 
60 
61 

49 
67 
64 

73 
60 
45 

60 
11 
41 

73 
95 
63 

73 
62 

77 

98 
97 
68 

93 
97 
79 

71 
87 
62 

83 
81 
50 

78 
83 
66 

24 
33 
18 

93 
94 

81 

93 

78 
71 

97 
96 
90 

97 
98 

88 

80 
82 
71 

64 
74 

89 

83 
72 
79 

14 
33 
26 

97 
100 

88 

73 
83 
84 

100 
100 

86 

97 

98 

100 

97 
83 
79 

96 

84 
80 

80 
78 
81 

65 
53 
51 

95 

IV 

97 

V 

89 

believe 

III 

85 

IV 

78 

V 

72 

cousin 

III 

100 

IV 

100 

V 

91 

know 

III 

100 

IV 

100 

V 

96 

ninety 

III 

80 

IV 

86 

V 

74 

pigeons 

III 

86 

IV 

95 

V 

saucer 

III 

84 
75 

IV 

78 

V 

78 

too 

III 

32 

IV 

45 

V 

39 

The  first  list  will  be  called  the  "  First  Preferred  List."     It 


contains  the  following  words: 

1.  even  lo.  forty 

2.  lesson  II.  pretty 

3.  only  12.  wear 

4.  smoke  13.  button 

5.  front  14.  minute 

6.  sure  15.  cousin 

7.  pear  16.  nails 

8.  bought  17.  janitor 

9.  another 


18.  saucer 

19.  stopping 

20.  sword 

21.  freeze 

22.  touch 

23.  whistle 

24.  carriage 

25.  nor 


The  Preferred  Lists 


13 


The  second  list, 

called  the  "  Second 

Preferred  List," 

is  as 

follows  : 

I.  already 

10.  tailor 

i8.  whole 

2.  beginning 

II.  telegram 

19.  against 

3.  chicken 

12.  telephone 

20.  answer 

4.  choose 

13.  tobacco 

21.  butcher 

5.  circus 

14.  too 

22.  guess 

6.  grease 

15.  towel 

23.  instead 

7.  pigeons 

16.  Tuesday 

24.  raise 

8.  quarrel 

17.  tying 

25.  beautiful 

9.  saucy 

Table  III  gives  for  each  word  of  the  First  Preferred  List 
and  for  each  grade  the  number  of  times  the  word  was  written, 
the  number  of  times  it  was  spelled  correctly,  and  the  per  cent 
correct.  Schools  I,  II,  III,  IV,  and  V  are  included.  (Omitted 
words  are  considered  as  "  written  "  and  as  wrong.)  Table  IV 
gives  the  same  facts  for  the  Second  Preferred  List. 

It  will  be  seen  from  tables  III  and  IV  that  for  any  given 
word  the  per  cent  correct  in  one  grade  is  higher  than  it  is  in 
any  lower  grade.  This  is,  of  course,  to  be  expected.  But  it 
is  not  sufficient.  In  order  that  this  list  should  be  of  greatest 
value  it  should  be  so  constituted  that  these  increases  in  '  per- 
cents-correct '  so  keep  pace  with  the  increase  from  grade  to 
grade  of  general  spelling  ability  that  a  word  tends  in  all  grades 
to  maintain  the  same  difficulty  relative  to  all  other  words  in  the 
list  to  which  it  belongs.  A  word  which  is  20th  in  point  of  diffi- 
culty for  the  3d  grade  ought  to  deviate  as  little  as  possible  from 
the  same  rank  in  the  other  grades.  The  experience  gained  in 
making  this  investigation  leads  us  to  think  that  most  words 
do  not  meet  this  condition  even  approximately.  The  span  be- 
tween the  3d  and  the  8th  grades  is  very  wide.  Accordingly  a 
very  large  class  of  words  is  impossible  for  the  earlier,  yet  easy 
for  the  later,  grades.  Still  others  are  really  difficult  in  the  lower 
grades  but  of  almost  no  difficulty  in  the  upper  grades.  From 
our  own  Original  List  "  coffee "  and  "  people "  are  hard  for 
3d-  and  4th-graders,  but  are  almost  always  spelled  correctly 
above  the  6th  grade.  A  third  group  of  words  breaks  down  in 
the  middle.     They  appear  to  be  easy  in  the  lowest  and  highest 


14       Spelling  Ability — Its  Measurement  and  Distribution 


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i6       Spelling  Ability — Its  Measurement  and  Distribution 

and  hardest  in  the  middle  grades.  "  Whose  "  is  a  type  of  such 
a  word.  It  presents  no  great  difficulty  until  children  learn  the 
use  of  the  apostrophe.  Then  they  write  "  who's."  Later  they 
partly  recover  from  this  practice.  There  are  quantities  of  words 
which  show  this  dip  in  the  middle  grades.  One  homonym  is 
often  easy  until  the  other  has  been  consciously  related  to  it. 
Analogies  falsely  assumed  play  a  harmful  role.  The  rapid  en- 
riching of  the  vocabulary  as  new  subjects  and  new  phases  of 
old  subjects  are  taken  up  in  the  middle  grades  probably  induces 
some  confusion.  To  just  what  extent  this  is  true  we  do  not 
know  but  we  are  sure  that  it  is  true  to  a  significant  degree. 

Finally,  we  have  the  large  class  of  words  which — when  a 
sufficient  number  of  children  are  tested — do  show  an  increase 
in  correctness  from  grade  to  grade,  but  which  do  not  advance 
in  anything  like  a  constant  ratio  to  the  advance  from  grade  to 
grade  in  spelling  ability.  Even  among  the  words  chosen  as  most 
favorable  this  discrepancy  may  be  seen.  The  word  "  sure " 
(Table  III)  is  47  per  cent  correct  in  the  3d  grade.  This  gives 
it  a  rank  of  6th  among  the  25  words  of  the  First  Preferred  List 
for  that  grade.  In  the  4th  grade  it  advances  to  55  per  cent 
correct,  but  this  advance  is  not  sufficient  to  maintain  its  position. 
It  falls  to  a  rank  where  it  is  tied  with  "  whistle  "  for  nth  and 
I2th  place — i.e.,  its  rank  is  11.5.  In  the  5th,  6th,  7th,  and  8th 
grades  its  rank  remains  fairly  constant  with  the  4th-grade  rank. 
It  is  10.5,  14.5,  10.5,  and  12. 

If  this  sort  of  irregularity  is  found  in  a  word  chosen  as  among 
the  most  regular,  it  will  easily  be  seen  how  much  greater  would 
be  the  irregularity  of  words  which  were  rejected. 

§  6.    Examination  of  the  First  Preferred  List 

To  further  establish  the  value  of  the  lists,  we  may  investigate 
the  behavior  of  the  words  as  between  grades  in  each  school 
and  in  all  schools  combined.  We  shall  begin  with  the  First 
Preferred  List.  This  list  was  chosen  in  the  first  instance  from 
the  returns  of  School  I.  It  was  taken  to  be  the  25  words  of 
closest  correlation  between  the  grades  of  that  school.  It  was 
then  referred  to  the  other  schools  and  the  correlations  were 
worked  out  for  them. 


Examination  of  the  First  Preferred  List 


17 


The  method  used  was  that  suggested  by  Spearman  in  his 
article:  "'Foot-rule'  for  Measuring  Correlation"  (Spearman, 
'06).  This  method  is  explained  and  criticised  by  Brown  in 
"The  Essentials  of  Mental  Measurement,"  pp.  71-76  (Brown, 
'11),  and  in  a  more  elementary  way  by  Whipple  in  his  "  Man- 
ual," pp.  34  and  35.     (Whipple,  '10.) 

The  formula  is 

i/6(A^2  — I) 
where  2(^)  denotes  the  sum  of  the  "gains"  in  rank  (sum  of 
positive  differences)  of  the  second  series  on  the  first,  and  1/6 
(N^  —  i)  is  the  value  of  the  simi  of  such  gains  which  may  be 
expected  by  chance.  These  i?-values  were  then  expressed  as 
r-values  (Pearson  Coefiicients  of  Correlation)  by  means  of  a 
table  of  equivalents.    This  table  (Whipple,  '10,  p.  36),  has  been 

TT 

worked  out  from  Spearman's  conversion  formula  r  =  sin  (—  R). 

2 
The  method  is  illustrated  for  the  4th  and  5th  grades  of  School 
I  in  Table  V. 

By   the  formula,  R  =  i ,  R  =  .72.     This   is 

i/6(iV2  — i) 
equivalent  to  an  r-value  of  .90.     The  correlation  is  therefore 
very  satisfactory.    Its  Probable  Error  is  ,026,  which  is  so  small 
in  relation  to  the  obtained  correlation,  that  the  latter  has  a  very 
high  degree  of  reliability. 

The  correlation  of  each  grade  with  every  other  grade   for 
School  I  was  as  follows : 


Correlation  of  4th  grade  with  5th  grade. 


4th 
4th 
5th 
5th 
6th 


"  6th 
"  7th 
"  6th 
"  7th 
"  7th 
Average. 


90 
88 
88 
92 

93 
88 
90 


(P.E.  =  .026) 


[8       Spelling  Ability — Its  Measurement  and  Distribution 


TABLE  V 

School  I.     Coefficients  of  Correlation  for  4th  and  5th 
Grades  Derived.     Foot-rule  Method 


4th  Grade 

5th  Grade 

Gains, 
5th  on  4th 

%           Rank 

%           Rank 

90            1 
80           2 
77           3.5 
77           3.5 
70           5.5 

70           5.5 
69           7 
67           8 
65           9 
63          10.5 

63         10.5 
56          12 
50          13 
49          14 
42          15.5 

42          15.5 
40          17.5 
40          17.5 
30          19 
25         20 

21          22 
21          22 
21          22 
17         24 
13          25 

94           2 
85           4.5 
96           1 
81           7 
75         11 

85           4.5 
77         10 
83           6 
79           8.5 

72  13 

89           3 

73  12 
70          14 
65          16 
65         16 

79           8.5 
56          19 
65         16 
47         23 
50          22 

63         18 
52          21 
55         20 
45         24 
43         25 

1 

2.5 

3.5 

5.5 

3 

another 

foi^^^v           

2.5 

Drettv 

wear      

button      

1 

minute      

2 

cousin 

.5 

janitor          

1.5 

saucer 

stopping 

4 

2 

freeze  

touch  

nor    

29  =  2(g) 

It  may  be  interesting  before  taking  up  the  results  in  other 
schools  to  see  to  what  extent  the  '  foot-rule '  method  justifies 

itself  in  this  kind  of  work.    The  '  product-m.oment '  (r= ) 

tuxiaz 
and  the  'unlike  signs'  methods  (r  =  cos  ttv)  were  used  as  a 
check.    Table  VI  shows  the  result. 

It  is  evident  from  Table  VI  that  if  the  true  numerical  state- 
ment of  the  amount  of  correlation  may  be  expected  to  be  at 
or  near  the  average  of  all  three  methods,  the  one  which  tends 
most  nearly  to  approximate  the  true  result  is  here  the  '  foot-rule ' 


Examination  of  the  First  Preferred  List 


19 


TABLE  VI 
r-VALUES  Between  Grades  of  School  I  as  Found  by  Three  Methods 


Pairs  of  Grades 

Foot-rule 

Product- 
moment 

Unlike 

signs 

Average 

4th  with  5th 

.90 

.88 
.88 
.92 
.93 

.88 

.92 

.76 
.73 

.78 
.79 
.91 

.99 
.97 
.81 
.99 
.88 
.93 

94 

4th     "     6th 

87 

4th     "     7th 

.81 

5th     "     6th 

.90 

5th     "     7th 

87 

6th     "     7th 

91 

Averages 

.90 

.82 

.93 

.88 

method.  It  has  therefore  seemed  justifiable  in  future  computa- 
tions of  this  sort  to  save  the  threefold  labor  and  to  rely  upon 
this  method. 

It  is  to  be  expected  that  since  the  list  of  words  was  in  the  main 
selected  from  the  results  in  School  I,  the  correlation  will  prove 
to  be  higher  in  that  school  than  in  any  other.  Such  is  indeed 
the  case  as  will  be  seen  by  an  inspection  of  Table  VII.  It  will 
be  remembered  that  School  I  has  no  8th  grade  and  that  the 
3d  grade  in  that  school  was  not  tested. 

We  find  that  the  correlations  in  School  II  are  considerably 
lower  than  in  schools  III,  IV,  and  V,  even  showing  an  apparent 
inverse  relation  in  one  instance.  Yet  the  average  of  the  coeffi- 
cients for  School  II  is  .42,  the  P.E.  of  which  is  less  than  .11. 
A  correlation  is  entitled  to  scientific  consideration  if  it  is  more 
than  twice  as  large  as  its  probable  error.  This  one  is  nearly 
four  times  its  probable  error,  and  may  therefore  be  regarded 
as  satisfactory.  Still  more  so  are  the  relations  between  grades 
in  the  other  schools ;  while,  for  all  schools  combined,  the  coeffi- 
cients of  grade-to-grade  correlation  range  from  .47  to  .93  with 
an  average  of  .76,  A.D=.I2.  Since  for  these  same  values 
P.E.  ranges  from  .10  to  .02  with  an  average  at  .057,  the 
reliability  of  these  values  is  adequate. 

It  appears  therefore  that  this  list  of  words  possesses  the 
advantage  of  maintaining  practically  the  same  order  of  difficulty 
throughout  the  grades  from  the  3d  to  the  8th.  In  any  grade 
the  hardest  word,  the  easiest  word,  and  the  words  which 
take  rank  between  tend  strongly  to  hold  their  positions  in  every 


20       Spelling  Ability — Its  Measurement  and  Distribution 

other  grade.    Our  list  then  is  to  a  marked  degree  independent  of 
fluctuations  between  grades. 

But  this  might  be  true  and  still  leave  something  to  be  desired. 
Schools  differ  in  many  respects — in  quality  of  teaching  and 
supervision,  in  preferred  methods,  in  word  lists  studied,  in  the 
character  of  the  children  as  to  economic  and  racial  condition. 
The  schools  which  we  have  under  consideration  differ  widely 
in  all  those  respects.  These  variations  in  local  conditions  may 
very  likely  produce  considerable  variation  in  the  quality  of  the 
spelling  output. 

TABLE  VII 

Coefficients  of  Correlation.    Grade  with  Grade,  and  Each 

Grade  with  All  Grades  for  Each  School.    First 

Preferred  List 


School 

3d  with  4th 

"      "     5th 

"      "     6th 

"      "     7th 

"      "     8th 

"      "     entire  school 

4th     «  5th 

"       "  6th 

"  7th 

"       "  8th 

"       "  entire  school 

5th  "  6th 

«  "  7th 

"  "  8th 

"  "  entire  school 

6th     "     7th 

"       "     8th 

"       "     entire  school 

7th     "     8th 

"       "     entire  school 

8th     "     entire  school 

Average,  grade  with  grade. 

Average,  grade  with  school 


II 

III 

IV 

V 

.37 

.78 

.67 

.69 

.25 

.55 

.31 

.71 

—  .07 

.40 

.45 

.75 

.40 

.23 

.34 

.75 

.01 

.31 

.47 

.67 

■35 

■79 

■77 

■85 

.81 

.59 

.61 

.89 

.54 

.59 

.62 

.84 

.37 

.37 

.60 

.73 

.20 

.34 

.62 

.77 

■78 

.84 

■84 

92 

.72 

.60 

.90 

.93 

.60 

.69 

.88 

.90 

.52 

.48 

.83 

.72 

.91 

■84 

.82 

■95 

.56 

.66 

.94 

.89 

.62 

.60 

.85 

.89 

■77 

■77 

■84 

■93 

.45 

.76 

.90 

.80 

■75 

.61 

■78 

.89 

.60 

■57 

.82 

.81 

.42 

.53 

.67 

.80 

.69 

■74 

.81 

.89 

All  schools 


.79 
.71 
.55 
.47 
.71 
.82* 

.83 
.69 
.62 
.72 
.90* 

.90 

.86 
.93 
.98* 

.90 
.89 
.88* 

.89 
.86* 

.91* 

.76 

.89* 


*  These  r-values  are  for  each  grade  with  the  grades  of  all  schools 


Examination  of  the  First  Preferred  List 


21 


TABLE  VIII 

Correlations  op  School  with  School  and  of  Each  School  with 
All  Schools  for  Each  Grade.     First  Preferred  List 

School  I  is  not  included  because  of  its  different  system  of  grading 


Grades 

School    II  with  III 

II     "      IV 

II     "       V 

II     "     All 

"       III     "      IV 

"       III     "       V 

"       III     "     All 

IV     "       V 

IV     "     All 

V     "     All 

Average,  school  with  school 

Average,  each  school  with  all 
schools 


3d 

grade 


77 
S3 

S3 
58 

■79 


4th 
grade 


.60 
.74 

.82 
.76 

.66 

.77 


.75 
.84 

.86 

.72 

.84 


5th 
grade 


89 


6th 
grade 


•S3 


7th 
grade 


.82 


8th 
grade 


All 
grades 


.70 
.80 

.88 
.gi* 

88 
81 
87* 

85 
93* 

93* 

82 


■73       91* 


♦These  figures  are  for  each  school  with  all  grades  and  schools  comhined,  i.e.,  with  all 
participants. 

A  method  in  reading  and  word  study  which  makes  extensive 
use  of  the  phonogram  may  possibly  cause  some  words  to  become 
easy  which  are  otherwise  difficult.  If  the  pupils  in  one  school 
come  from  homes  where  English  is  not  spoken,  they  may  find 
difficult  a  set  of  words  other  than  that  which  children  of  English- 
speaking  parents  find  difficult. 

With  the  purpose  of  throwing  some  light  on  this  point  we 
shall  consider  what  the  correlation  is  between  schools  for  each 
grade  and  for  all  grades  with  respect  to  the  First  Preferred  List. 
Table  VIII  shows  the  correlation  coefficients.  The  school-with- 
school  average  correlations  range  from  .48  to  .82  with  a  median 
at  .69.  The  school-with-all-school  averages  range  from  .y^  to 
.91  with  a  median  at  .83.  A  few  of  the  coefficients  throughout 
the  table  are  low.  There  are,  however,  but  six  that  are  below 
.50.  All  but  one  of  these  are  in  the  extreme  grades  (3d  or  8th) 
and  have  to  do  with  School  II.  The  circumstances  under  which 
this  school  was  examined  account  for  this.    The  tests  were  given 


22       Spelling  Ability — Its  Measurement  and  Distribution 

immediately  after  the  long  summer  vacation  and  the  test-material 
comprised  the  Original  List  (270  words).  The  other  schools 
were  tested  considerably  later  in  the  school  year  and  the  pupils 
in  those  schools  wrote  the  Selected  List  (100  words). 

Notwithstanding  these  few  shortcomings  the  70  coefficients 
of  Table  \TII  form  an  impressive  argument  for  the  value  of  the 
First  Preferred  List,  We  may  fairly  contend  that  not  only 
are  the  positions  of  the  words  of  this  list  relatively  stable  as 
between  grades  (Table  VII),  but  that  this  permanency  holds  as 
between  schools. 


§  7.    Examination  of  the  Second  Preferred  List 

The  second  list  of  25  words  (see  p.  13  or  Appendix  II)  was 
examined  in  the  same  way  that  the  first  list  was  examined,  i.e., 
with  reference  to  correlations  first  between  grades,  and  second 
between  schools. 

At  School  I  the  correlations  between  grades  were  found  to  be 
as  follows  (Compare  with  similar  tabulation  for  the  First  Pre- 
ferred List  on  page  17: 


4th  grade 

with  5th  grade  .87 

4th 

"     6th      "       .83 

4th      " 

"      7th      "       .79 

5th      " 

"     6th      "       .95 

5th       " 

"      7th      "       .78 

6th      " 

"      7th      "       .83 

Average 84 

(P.E.=.04) 

For  the  other  schools  Table  IX  shows  the  correlations.  It 
may  be  compared  with  Table  VII   (page  20). 

A  comparison  of  Table  IX  with  Table  VII  shows  that 
although  the  word  list  to  which  Table  IX  refers  was  taken,  on 
the  basis  of  partial  knowledge,  to  be  somewhat  inferior  to  the 
First  Preferred  List,  these  coefficients  do  not  show  it.  The 
grade-with-grade  averages  (.66,  .67,  .60,  .48,  and  .75)  are  higher 
for  some  schools  than  in  Table  VII  and  lower  for  others.  Their 
central  tendency  is  almost  identical  while  the  closeness  of  group- 
ing is  greater  for  the  second  than  for  the  first  list.     Of  the 


Examination  of  the  Second  Preferred  List 


23 


105  measures  of  correlation  in  Table  IX  only  13  are  less  than 
four  times  their  probable  error,  and  only  3  are  less  than  twice 
their  probable  error.  The  grade-to-grade  relationships  for  all 
schools  (column  6)  range  from  .40  to  .95,  average  .75,  A.D.= 
.14.  This  is  satisfactory  to  a  degree  scarcely,  if  at  all,  less  than 
is  the  showing  for  the  first  list. 


TABLE  IX 

Coefficients  of  Correlation.     Grade  with  Grade  and  Each 

Grade  with  All  Grades  for  Each  School.     Second 

Preferred  List 


School 

3d  with  4th 

"      "     5th 

"      "     6th 

"      «     7th 

"      "     8th 

"      "     entire  school 

4th  "  5th 

"  "  6th 

"  "  7th 

"  «  8th 

"  "  entire  school 

5th  "  6th 

«  "  7th 

"  "  8th 

"  "  entire  school 

6th     "     7th 

"       "     8th 

"       "     entire  school 

7th     "     8th 

"       "     entire  school 

8th     "     entire  school 

Average,  grade  with  grade. 

Average,  grade  with  school 


II 

III 

IV 

V 

.60 

.75 

.55 

.38 

.69 

.62 

.56 

.26 

.61 

.55 

.55 

.11 

.43 

.55 

.41 

.07 

.51 

.52 

.35 

—  .01 

■73 

.84 

■75 

■34 

.73 

.82 

.69 

.48 

.74 

.61 

.44 

.40 

.60 

.62 

.45 

.38 

.57 

.60 

.51 

.38 

.82 

.88 

■78 

.67 

.75 

.76 

.74 

.84 

.55 

.75 

.73 

.65 

.62 

.73 

.72 

.83 

.81 

.92 

.90 

.92 

.83 

.67 

.79 

.76 

.82 

.71 

.77 

.84 

■93 

.82 

■84 

.88 

.80 

.80 

.74 

.86 

.88 

■83 

.80 

■78 

.89 

.80 

.81 

.86 

.66 

.67 

.60 

.48 

.84 

.87 

.81 

■74 

All  schools 

.74 
.73 
.55 
.40 
.41 
.72* 

.90 
.80 
.69 
.62 
■93* 

.90 
.83 
.80 
■95* 

.94 
.89 
.91* 

.90 

.87* 

.80* 
.75 

.86* 


*  These  r-values  are  for  each  grade  with  all  grades  of  all  schools. 

Table  X  (whose  counterpart  for  the  first  list  is  Table  VIII) 
reveals,  as  Table  IX  did  not,  the  relative  inferiority  of  the 
second  list.  There  are  49  coefficients  in  Table  X  that  are  lower 
than   the  corresponding  figures   in   Table  VIII.     Only  21   are 


24       spelling  Ability — Its  Measurement  and  Distribution 


higher.  The  school-with-school  averages  are  lower  in  five 
instances  and  higher  in  but  two.  The  order  of  difficulty  of 
these  words  is  therefore  not  so  permanent  as  between  schools. 
It  is,  how-ever,  sufficient  abundantly  to  justify  the  list.  There 
are  but  six  of  the  70  coefficients  in  the  body  of  the  table  that 
are  less  than  four  times  their  probable  error,  and  but  three  that 
are  less  than  twice  their  probable  error.  In  some  respects, 
indeed,  this  list  is  superior  to  the  first  list.     A  comparison  of 

TABLE  X 

Correlations  of  School  with  School  and  of  Each  School  with 

All  Schools  for  Each  Grade.     Second  Preferred  List 

School  I  not  included.     Compare  with  Table  VIII,  p.  21 


School    II  with  III 

II     "      IV 

II     "       V 

II     "     All 

"       III     "      IV 

"       III     "       V 

"       III     "     All 

IV     "       V 

IV     "     All 

V     "     All 

Average,  school  with  school 

Average,  each  school  with  all 
schools 


3d 
grade 


.69 


4th 
grade 


51 
17 
08 
56 

38 
43 
78 

43 

76 

57 
31 

.68 


5th 
grade 


82 
62 
78 

55 

74 

82 
58 

.80 


6th 

grade 


59 

75 

65 
61 

■79 


7th 
grade 


8th 
grade 


66 

69 

88 
62 

.<^7 


All 
grades 


.66 
.43 
.60 


.59 

.87 
.88* 

.65 

■77* 

.78* 
.63 

.82* 


♦These  figures  are  for  each  school  with  all  grades  and  schools  combined,  i.e.,  with  all 
participants. 

Tables  III  and  IV  shows  that  the  words  of  the  second  list  are 
in  general  more  difficult  than  those  of  the  first.  Doubtless  the 
first  list  is  a  somewhat  better  test  for  lower  grades,  while  the 
second  is  a  better  test  for  upper  grades.  This  supposition  is 
neatly  supported  by  the  figures  in  Table  X.  Sixteen  of  the  21 
that  are  higher  in  this  table  than  in  Table  VIII  are  in  the  three 
upper  grades,  while  the  two  higher  average  correlations  are  in 
the  7th  and  8th  grades.  If,  therefore,  some  of  the  words  in  the 
first  list  are  found  to  be  too  easy  for  the  highest  grades — as 


Conclusions  Regarding  the  Preferred  Lists  25 

doubtless  they  may  be — then  the  second  list  will  supply  a  valuable 
supplement  to  the  first. 

§  8.     Conclusions  Regarding  the  Preferred  Lists 

Our  lists  therefore  prove  to  be  well  selected.  Success  and 
failure  in  spelling  them  may  be  used  with  considerable  confidence 
to  measure  the  thing  we  call  spelling  ability.  The  establishment 
of  this  fact  is  of  the  utmost  importance.  In  general  when  we 
are  to  measure  mental  traits  or  capacities  the  thing  we  directly 
measure  is  itself  a  physical  phenomenon  or  fact.  We  measure 
fatigue  by  the  number  and  height  of  lifts  with  the  ergograph,  or 
by  the  distajice  between  points  of  the  esthesiometer  necessary  to 
be  recognized  as  '  two.'  We  measure  attention  and  perception 
by  counting  dots  or  by  cancellation ;  memory,  by  the  number  of 
digits  reproduced ;  association  by  the  number  of  words  pro- 
nounced in  a  given  time;  and  intelligence  itself,  by  a  series  of 
tests  which  may  be  scored  objectively.  What  we  deal  with 
directly  is  something,  assumed  to  be  functionally  related  to  the 
trait  in  question,  which  can  be  measured  in  time  or  space  or 
which  can  be  counted.  If  this  objective  manifestation  does  not 
accurately  register  the  subjective  state  to  which  it  is  supposed 
to  correspond,  it  is  impaired,  to  the  extent  of  its  inaccuracy,  as 
an  index  to  be  directly  measured. 

Now  it  is  undoubtedly  true  that  the  misspellings  of  most  words 
are  unreliable  as  indicating  lack  of  spelling  ability  in  general ; 
and  on  the  other  hand  it  is  probable  that  to  spell  them  correctly 
often  argues  little  more  than  that  the  subject  can  spell  the 
particular  words  that  he  did  spell.  Most  words  are  in  some  way 
special — and  they  are  special  (particularly  for  children)  in  ways 
that  we  do  not  realize.  Very  often  they  do  not  mean  the  same 
thing  to  one  person  that  they  do  to  another.  They  are  frequently 
pronounced  differently  by  different  people.  They  suggest  dis- 
similar imagery.  They  connote  variously.  They  range  from 
very  easy  to  very  hard ;  and  those  that  are  easy  for  some  people 
are  hard  for  others.  Moreover  there  are  numerous  ways  of 
misspelling  them,  each  indicating  its  own  causal  incoordination. 
An  error  may  not  be  equal  to  an  error  even  in  misspelling  the 
same  word. 


26       spelling  Ability — Its  Measurement  and  Distribution 

It  would  be  presumptuous  to  suppose  that  all  these  difficulties 
have  been  overcome  in  selecting  our  two  preferred  lists.  Without 
doubt  we  have  only  roughly  approximated  the  ideal  conditions 
under  which  a  physical  fact  may  be  the  transcript  of  a  mental 
trait.  Probably  nothing  more  satisfactory  than  an  approxima- 
tion can  be  devised.  But  we  have  been  at  no  small  pains  to 
secure  a  list  of  words  which  would  be  free  from  many  of  these 
variations,  and  we  think  we  have  done  so.  From  an  inspection 
of  them  we  may  be  justified  in  believing  that  their  pronunciation 
and  meaning  are  fairly  constant  for  everybody;  and  we  may 
regard  it  as  probable  that  their  associative  connections  do  not 
vary  much  for  different  people.  From  a  statistical  analysis  of 
them  we  find  that  their  behavior  with  elementary  school  children 
is  constant  to  a  marked  degree,  and  in  particular  that  it  is  relative- 
ly independent  of  maturity  and  of  local  conditions.  Older 
children  in  higher  grades  spell  them  more  frequently  and  in  each 
grade  more  frequently  than  in  the  one  before  it.  Children  in 
schools  under  favorable  circumstances  do  better  with  them  than 
do  children  in  less  favorable  situations.  It  is  because  they  re- 
flect these  conditions  that  they  are  valuable.  By  the  use  of 
them,  conditions  in  a  school,  a  class,  or  an  individual  may  be 
revealed ;  and  conversely  to  a  certain  extent  if  the  conditions  are 
known  (e.g.,  the  grade)  the  results,  by  the  use  of  them,  are  pre- 
dictable. 

These  lists,  then,  tend  strongly  to  remain  intact  under  various 
conditions.  As  lists  they  appear  to  be  reliable,  and  our  numerical 
results  give  quantitative  expression  to  this  reliability.  But  as 
to  the  words  themselves,  we  shall  yet  have  much  to  say.  There 
has  been  no  attempt  to  secure  lists  composed  of  words  of  equal 
difficulty.  The  effort  has  rather  been  to  choose  words  which 
differ  widely  in  this  respect.  We  shall  now  attempt  to  arrange 
these  words  on  a  scale  which  shall  accurately  represent  their 
difficulty,  assuming  as  true  a  certain  supposition  concerning  the 
form  of  distribution  of  spelling  ability  within  a  school  grade. 
The  resulting  scale  will  represent  their  difficulty  approximately 
in  so  far  as  this  supposition  is  approximately  true.  When  this 
is  done,  their  value  for  test  purposes  independently  of  the  list 
which  contains  them  will  be  established. 


Ratings  of  Individual  Pupils 


27 


§  9.     Ratings  of  Individual  Pupils 

In  addition  to  scoring  words,  the  papers  of  individual  pupils 
were  rated.  This  was  done  in  the  usual  manner,  the  ability  to 
spell  one  word  being  scored  as  equal  to  the  ability  to  spell  any 
other  word  of  the  list.  This  procedure  is  subject  to  the  criticism 
made  in  Section  i  above;  but  in  the  absence  of  any  evaluation 
of  the  words,  a  system  of  weighting  is  not  possible.  The  results 
will  not  be  misused  here. 

The  test  material  consisted  of  the  100  words  of  the  Selected 
List.  The  papers  written  at  schools  II,  III,  IV,  and  V  were 
used.  School  I  was  not  available  because  of  its  system  of  grad- 
ing. A  few  papers  were  incomplete  in  each  of  the  schools ;  these 
were  rejected  in  this  part  of  the  work.  In  all,  2,487  papers  were 
rated.     Table  XI  shows  for  each  grade  the  distribution  of  in- 


TABLE  XI 

Distribution  of  Individual  Ratings  of  Pupils  in 
Schools  II,  III,  IV  and  V 


Per- 

centage 
Correct 

3d  Grade 

4th  Grade 

5th  Grade 

6th  Grade 

7th  Grade 

8th  Grade 

No. 

% 

No. 

% 

No. 

% 

No. 

% 

No. 

% 

No. 

% 

0-    5 

9 

2.0 

1 

.2 

1 

2 

6-  10 

22 

4.9 

1 

.2 

2 

.4 

11-  15 

30 

6.7 

10 

2.1 

1 

2 

16-  20 

38 

8.5 

12 

2.6 

9 

A 

21-  25 

44 

9.9 

13 

2.8 

6 

1.2 

2 

.5 

26-  30 

47 

10.6 

23 

4.9 

12 

2.3 

31-  35 

34 

7.6 

29 

6.2 

13 

2.5 

2 

.5 

2 

.5 

36-  40 

38 

8.5 

27 

5.8 

11 

2.1 

41-  45 

24 

5.4 

30 

6.4 

18 

3.5 

6 

1.4 

2 

.5 

46-  50 

34 

7.6 

33 

7.1 

28 

5.4 

4 

1.0 

1 

.3 

51-  55 

26 

5.8 

27 

5.8 

20 

3.9 

6 

1.4 

3 

.8 

56-  60 

24 

5.4 

31 

6.6 

32 

6.2 

15 

3.6 

5 

1.4 

1 

.4 

61-  65 

26 

5.8 

39 

8.4 

44 

8.5 

12 

2.9 

6 

1.6 

1 

.4 

66-  70 

17 

3.8 

29 

6.2 

48 

9.3 

23 

5.5 

8 

2.2 

3 

1.1 

71-  75 

13 

2.9 

45 

9.6 

49 

9.5 

30 

7.2 

18 

4.9 

8 

2.9 

76-  80 

8 

1.8 

35 

7.5 

59 

11.5 

52 

12.4 

31 

8.5 

11 

4.0 

81-  85 

4 

.9 

33 

7.1 

37 

7.2 

67 

16.0 

38 

10.4 

19 

6.9 

86-  90 

4 

.9 

26 

5.6 

64 

12.4 

61 

14.6 

79 

21.6 

41 

14.8 

91-  95 

3 

.7 

19 

4.1 

50 

9.7 

101 

24.2 

93 

25.5 

80 

28.9 

96-100 

4 

.9 

18 

3.5 

37 

8.9 

79 

21.6 

113 

40.8 

Totals... 

445 

467 

515 

418 

365 

277 

Medians. 

35.8 

60.70 

73.10 

84.90 

90.50 

94.68 

A.  D.... 

18.0 

20.9 

10.4 

10.0 

7.9 

5.8 

2  8         spelling  Ability — Its  Measurement  and  Distribution 


dividual  ratings.  It  reads  as  follows :  "In  the  3d  grade  9  pupils 
were  rated  between  0%  and  5%,  which  was  2.0%  of  all  the  3d 
grade  pupils.  In  the  4th  grade  i  pupil  was  rated  between  0% 
and  5%,  which  was  .2%  of  all  the  4th  grade  pupils,"  etc. 

The  striking  characteristic  of  the  distribution  of  these  ratings 
is  their  extreme  variability.  Children  of  the  3d  grade  are  repre- 
sented in  every  group  but  one,  while  children  of  the  4th  and  5th 
grades  are  rated  in  every  group.  It  appears  that  we  may  expect 
a  few  6th-  and  /th-grade  children  to  spell  not  more  than  20  or 
30  of  these  hundred  words,  which  is  not  quite  as  good  as  the 
typical  ability  of  3d-grade  children  for  the  same  words.  The 
8th-grade  pupils  show  the  least  variation.  This  is  probably 
true  of  this  grade  in  general.  It  is  not,  however,  as  marked  as 
these  figures  indicate.  The  100-word  list  as  a  whole,  whatever 
may  be  true  about  some  of  the  individual  words,  did  not  thorough- 
ly test  this  grade.  A  glance  at  Fig.  6  will  show  how  sharply  cut 
off  at  the  high  end  is  the  curve  of  distribution.  This  is  against 
all  the  facts  which  we  know  about  eighth-graders  in  particular 
and  human  ability  in  general.  A  harder  test  would  have  shown 
a  lower  mode  and  a  more  gradual  tapering  off  at  the  upper  end 
of  the  curve.  But  even  as  this  record  stands  we  may  look  for 
a  considerable  number — between  7  and  8  per  cent — of  Sth-grade 
pupils  to  average  no  better  than  the  typical  performance  of  5th- 
grade  children. 

TABLE  XII 
Distribution  of  Individual  Ratings  Grouped  to  Show  Modes.    Figs.  1-7 


Percentage 
Correct 

3d  Grade 

4th  Grade 

5th  Grade 

6th  Grade 

7th  Grade 

8th  Grade 

0-10    

6.9- 

15.2. 
20.5 
IG.l. 
13.0 
11.2 
9.6 
4.7 

22.1 
36.6 
24.2 
14.3 

2.5 

.4 

4.7 

7.T 

12.0. 

13. 5' 

12.4. 

14. 6' 

17.1. 

12.7] 

5.0J 

5.1 
19.7 
25.9 
31.7 

17.7 

4.6j 
8.9] 
10. ij 
17.8] 
21. oj 
19.6 
13.2. 

1.2 

8.1 

19.0 

38.8 

32.8 

"1   >.o 

.5J 

2.4] 

7.4 
5.OJ 

8.41 

28.0 
19. 6j 

.30.6] 

03.7 
.33.1  J 

.8' 

2.2. 

3.81 

13. 4J 

32.0 

47.1. 

.5 
3.0 

17.2 

79.1 

11-  20  

21-  30     

31-  40 

41-  50     

1 

51-  GO     

4I    ■' 

61-  70     

1.5] 

71-  80     

8.4 
6.9 

81-  90 

21.7] 

1  91.4 

f,9.7J 

91-100 

Ratings  of  Individual  Pupils 


29 


/o  20  30  vo  <ro  ^  70  So  90  ho 


0    /O  20  30  40  So  Co  70  so  90  700 

ff3.3. 


10  ZO  30  ^0  50  60  70  SO  <?0  WO 


O  /O  20  JO  W  ^0  60  70  80  90  /oo 


if 

20 


O    JO    Zo   Jo    w    So    Co    70    80   90    100 


Fig.  I 
Fig.  2 
Fig.  3 
Fig.  4, 
Fig.  5 


Frequency  of  each  rating   (of  per  cent  of  Selected  List  spelled 

correctly)  in  grade  3. 
Frequency  of  each  rating   (of  per  cent  of  Selected  List  spelled 

correctly)  in  grade  4. 
Frequency  of  each  rating   (of  per  cent  of  Selected  List  spelled 

correctly)  in  grade  5. 
Frequency  of  each  rating   (of  per  cent  of  Selected  List  spelled 

correctly)  in  grade  6. 
Frequency  of  each  rating  (of  per  cent  of  Selected  List  spelled 

correctly)   in  grade  7. 


30 


Spelling  Ability — Its  Measurement  and  Distribution 
70 
65 

Co 
S5 
60 
HS 

3S  Fig.  6 

30 
2S 
20 
IS 
JO 
5 


2S- 


0   10  20  30  iO  60  CO  70  80  ?0  lOO 


0   /o    2.0  30   i^o  so  ^0  70   80   90    joo 


Fig.  6.    Frequency  of  each  rating  (of  per  cent  of  Selected  List  spelled 

correctly)   in  grade  8. 

Fig.  7.     Frequency  of  each  rating   (of  per  cent  of  Selected  List  spelled 

correctly)  in  grades  3-8  combined. 


Overlapping  3 1 

Another  characteristic  of  the  distributions  shown  in  Table  XI 
is  the  absence  of  clearly  marked  modes.  Table  XII  is  a  group- 
ing of  the  per  cent  columns  of  Table  XI  into  lo's  and  20's.  From 
this  grouping  wide  modes  of  marked  character  are  shown. 

Figs.  I  to  7  show  the  same  facts  graphically.  From  the  nature 
of  these  figures  the  test  material  appears  to  have  been  capable 
of  revealing  satisfactorily  the  spelling  ability  of  grades  3,  4,  and 
5.  Figs.  I  to  7  are  the  surfaces  of  frequency  of  spelling  ability 
with  the  Selected  List.  In  each  of  them  the  horizontal  scale 
shows  percentages  correct ;  the  vertical  scale  shows  the  per  cent 
of  children  having  each  rating  for  percentage  correct,  by  steps 
of  10.  The  number  of  children  represented  is  445  in  grade  3, 
467  in  grade  4,  515  in  grade  5,  418  in  grade  6,  365  in  grade  7, 
and  277  in  grade  8. 

§  10.     Overlapping 

It  follows  as  a  matter  of  course  from  the  variability  of  these 
ratings  that  the  overlapping  of  grade  on  grade  is  conspicuous. 
We  have  located  the  median  abilities,  of  each  grade,  for  the 
selected  word  list.  They  are:  3d  grade,  35.8;  4th  grade,  60.7; 
5th  grade,  73.1  ;  6th  grade,  84.9;  7th  grade,  90.5 ;  8th  grade,  94.7 
(See  Table  XI).  Table  XIII  shows  the  number  of  pupils  and 
the  per  cent  of  pupils  in  each  grade  whose  ratings  equalled  or 
exceeded  the  medians  of  every  other  grade.  The  table  reads 
as  follows :  In  the  3d  grade  76  pupils  equalled  or  exceeded  the 
median  rating  of  the  4th  grade  which  was  17.1%  of  all  the  3d- 
grade  pupils ;  27  equalled  or  exceeded  the  median  rating  of  the 
5th  grade  which  was  6.1%  of  all  the  3d-grade  pupils.  In  the  4th 
grade  378  pupils  equalled  or  exceeded  the  median  rating  of  the 
3d  grade  which  was  80.9%  of  all  the  pupils  of  the  4th  grade, 
etc.  It  will  be  noticed  that  there  are  two  places  where  there  is 
no  overlapping.  There  are  no  3d-grade  children  who  equal  the 
median  rating  of  the  8th  grade,  although  the  3  who  exceed  the 
7th-grade  median  come  very  near  it.  Two  of  them  are  rated  at 
93  and  one  at  94,  only  1.7  and  .7  below  the  8th-grade  median. 
There  is  also  no  overlapping  of  the  8th  grade  on  the  3d.  All  the 
pupils  of  the  8th  grade  exceed  the  median  of  the  3d  grade.  When, 
however,  we  say  that  at  these  points  there  is  no  overlapping, 
we  do  not  mean  that  their  surfaces  of  frequency  do  not  enclose 


32         spelling  Ability — Its  Measurement  and  Distribution 

TABLE  XIII 

Number  and  Per  Cent  of  Pupils  in  Each  Grade  Whose  Ability 

Equalled  or  Exceeded  that  of  the  Median  Pupil 

IN  Every  Other  Grade 


3d  grade. . . 
N=445. .  .  . 
Med.=35.8 

4th  grade.  . 
N=467. .  .  . 
Med.=60.7 

5th  grade.  . 
N=515...  . 
Med.=73.1 

6th  grade.  . 
N=4l8. .  .  . 
Med.=84.9 

7th  grade.  . 
N=365. .  .  . 
Med.=90.5 

8th  grade.  . 

N=277. .  .  . 
Med.=94.7 


.3d 
Grade 

4th 
Grade 

5th 
Grade 

6th 
Grade 

7th 
Grade 

No. 

% 

76 
17.1 

27 
6.1 

9 
2.0 

3 
0.7 

No. 

% 

378 
80.9 

146 
31.3 

52 
11.1 

27 
5.8 

No. 

% 

478 
92.8 

370 

71.8 

142 
27.6 

73 
14.2 

No. 

% 

414 
99.0 

384 
91.9 

338 
80.1 

142 
34.0 

No. 

% 

363 
99.5 

354 
90.4 

328 
89.9 

256 
70.1 

No. 

% 

277 
100 

270 
99.0 

269 
97.1 

241 
87.0 

200 
72.2 

8th 
Grade 


9 
1.9 


30 
5.8 


57 
13.6 


99 
27.1 


common  areas.  If  Fig.  i  is  placed  on  Fig.  8  so  that  the  zero 
points  coincide,  it  is  evident  that  there  is  considerable  area  com- 
mon to  both.  We  mean  that  the  upper  part  of  the  3d-grade 
surface  of  frequency  does  not  lap  over  the  median  point  of  the 
8th-grade  surface,  and  that  the  lower  part  of  the  8th-grade  sur- 
face does  not  reach  down  to  the  3d-grade  median.  There  are 
many  3(l-grade  children  who  do  better  than  the  poorest  8th- 
grade  children. 

The  fact  is,  then,  that  except  as  between  the  3d  and  8th  grades, 
some  pupils  of  each  grade  perform  like  typical  children  of  every 
other  grade.  Since  this  is  true,  it  serves  to  fix  the  location  of 
the  frequency  curves  and  medians  for  each  grade  with  reference 
to  each  other.  For  the  purpose  of  doing  so  we  shall  for  the  pre- 
sent assume  that  the  distribution  of  spelling  ability  in  each  grade 
is  "normal,"  i.e.,  is  correctly  represented  by  the  curve  of  error. 

There  is  some  argument  for  this  assumption.     The  fact  that 


Overlapping 


33 


our  surfaces  of  frequency  (Figs.  i-6)  do  not,  especially  for  upper 
grades,  closely  resemble  the  normal  curve,  only  shows  that  the 
test  material  was  not  difficult  enough  to  bring  out  a  distribution 
in  real  accordance  with  spelling  ability.  The  result  of  using  a 
different  list  of  words  is  shown  for  grades  6,  7,  and  8  by  Figs. 
8,  9,  and  10.  The  test  material  in  this  instance  was  Rice's  "Sen- 
tence Test" :  396  children  in  the  6th  grade,  367  in  the  7th,  and 
244  in  the  8th  wrote  this  test  in  schools  II,  III,  and  VIII.    The 


0    /O  20  60  ^0  so  60  70  80  10  /OO 


30 
25 
20 
/$■ 
10 


0    /O  20  30  ^0  SO  (.0  70  &0  90  too  0    /O  20  30  fo  so  CO  70   30  90  100 

%^  ^lO. 

Figs.  8,  9  and  10.  Frequency  of  each  rating  (of  per  cent  of  Rice  Sen- 
tence List  spelled  correctly)  in  grades  6,  7  and  8,  respectively. 
A^=396  for  grade  6;  367  for  grade  7;  and  244  for  grade  8.  The 
horizontal  scale  is  for  per  cent  spelled  correctly;  the  vertical  scale 
is  for  the  percentage  of  children  receiving  each  rating  for  percentage 
correct,  by  steps  of  10. 

surface  of  frequency  for  the  6th  grade  is  close  to  the  "normal" 
surface.  If  that  for  the  7th  and  8th  grades  is  less  so,  it  is  still 
far  more  regular  than  the  surfaces  shown  for  these  grades  in 
Figs.  5  and  6  and  might  be  made  still  more  so  by  an  appropriate 
selection  of  test  material.     There  seems  no  good  ground  for  as- 


34         Spelling  Ability — Its  Measurement  and  Distribution 

suming  that  the  distribution  of  spelHng  abiHty  in  any  grade  is 
not  according  to  the  normal  curve  or  according  to  a  curve  which 
resembles  it  closely. 

§  II.  Location  of  Grade  Medians 
Upon  the  assumption,  therefore,  of  a  normal  distribution  we 
may  proceed  to  locate  the  grade  medians  with  reference  to 
each  other.  In  all  cases  we  shall  work  with  per  cents  instead  of 
with  numbers  of  pupils.  This  will  reduce  all  surfaces  of  fre- 
quency to  equal  areas.  We  shall  assume  further  that  the  real 
variability  of  any  one  of  these  grades  in  spelling  ability  is  equal 
to  the  real  variability  of  any  other  one  of  them. 

We  have  already  seen   (Table  XIII)   that  17.1%  of  the  3d- 


FiG.  II.     Showing  the  overlapping  of  the  3d  and  4th  grade  surfaces  of 

frequency. 

grade  pupils  equal  or  exceed  the  median  ability  of  4th-grade 
children.  Fig.  11  shows  this  fact  by  a  diagram.  The  surface 
on  the  left  (Axis  OM)  represents  the  3d-grade  distributions.  M 
is  its  median  point,  MD  (=MQ)  is  its  probable  error — i.e., 
figure  NPQD  is  one-half  its  area,  thus  graphically  representing 
one-half  the  cases  in  the  3d  grade,  which  accordingly  do  not 
deviate  from  the  median  by  an  amount  greater  than  MD.  The 
surface  on  the  right  represents  the  4th-grade  distribution  beyond 
whose  median  axis,  O'^M^,  the  3d-grade  surface  extends  to  an 
amount  represented  by  the  shaded  figure  KCM'^.  This  stands 
for  the  3d-grade  children  who  equal  or  exceed  the  4th-grade 
median — i.e.,  it  is  17.1%  of  the  3d-grade  surface  of  frequency. 
Accordingly  the  area  OKM'^M  represents  32.9%  of  the  cases. 
The  distance  MM^  may  now  be  found  in  terms  of  P.E.  It  is 
the  distance  from  the  median  point  along  the  .Y-axis  of  the  normal 
probability  integral  which  includes  32.9%  of  the  cases.    Distances 


Location  of  Grade  Medians 


35 


corresponding  to  different  per  cents  of  the  total  area  of  the 
curve  have  been  vi^orked  out.     Table  XIV,  which  is  taken  from 

TABLE  XIV 

Table  of  Values  op  the  Normal  Probability  Integral  Corre- 
sponding TO  Values  of  P.E,     Total  Area  of  the 
Surface  of  Frequency  Taken  as  10,000 


X 

X 

X 

X 

No. 

A 

No. 

A 

No. 

A 

No. 

A 

P.E. 

Ca.ses 

P.E. 

Cases 

P.E. 

Cases 

P.E. 

Cases 

81 

18 

0 

0 

135 

1.5 

3441 

80 

3.00 

4785 

17 

4.5 

49SS 

.05 

135 

134 

1.55 

3521 

76 

3.05 

4802 

15 

4.55 

4989 

.1 

269 

134 

1.6 

3597 

74 

3.1 

4817 

14 

4.6 

4990 

.15 

403 

133 

1.65 

3671 

71 

3.15 

4831 

14 

4.65 

4991 

.2 

536 

134 

1.7 

3742 

69 

3.2 

4845 

13 

4.7 

4992 

.25 

670 

132 

1.75 

3811 

65 

3.25 

4858 

12 

4.75 

4993 

.3 

802 

131 

1.8 

3876 

63 

3.3 

4870 

11 

4.8 

4994 

6 

.35 

933 

130 

1.85 

3939 

61 

3.35 

4881 

10 

4.85 

4994.6 

6 

.4 

1063 

130 

1.9 

4000 

57 

3.4 

4891 

9 

4.9 

4995.2 

5 

.45 

1193 

128 

1.95 

4057 

56 

3.45 

4900 

9 

4.95 

4995.7 

5 

.5 

1321 

126 

2.0 

4113 

53 

3.5 

4909 

8 

5.0 

4996.2 

4 

.55 

1447 

124 

2.05 

4166 

51 

3.55 

4917 

7 

5.05 

4996.6 

5 

.6 

1571 

124 

2.1 

4217 

48 

3.6 

4924 

7 

5.1 

4997.1 

3 

.65 

1695 

121 

2.15 

4265 

46 

3.65 

4931 

6 

5.15 

4997.4 

3 

.7 

1816 

119 

2.2 

4311 

43 

3.7 

4937 

6 

5.2 

4997.7 

3 

.75 

1935 

118 

2.25 

4354 

42 

3.75 

4943 

5 

5.25 

4998.0 

2 

.8 

2053 

115 

2.3 

4396 

39 

3.8 

4948 

5 

5.3 

4998.2 

2 

.85 

2168 

113 

2.35 

4435 

37 

3.85 

4953 

4 

5.35 

4998.4 

2 

.9 

2281 

111 

2.4 

4472 

36 

3.9 

4957 

4 

5.4 

4998.6 

2 

.95 

2392 

108 

2.45 

4508 

33 

3.95 

4961 

4 

5.45 

4998.8 

2 

1.0 

2500 

106 

2.5 

4541 

32 

4.0 

4965 

3 

5.5 

4999.0 

1.05 

2606 

103 

2.55 

4573 

29 

4.05 

4968 

3 

5.55 

4999.1 

1.1 

2709 

101 

2.6 

4602 

29 

4.1 

4971 

3 

5.6 

4999.2 

1.15 

2810 

98 

2.65 

4631 

26 

4.15 

4974 

3 

5.65 

4999.3 

1.2 

2908 

96 

2.7 

4657 

25 

4.2 

4977 

2 

5.7 

4999.4 

1.25 

3004 

93 

2.75 

4682 

23 

4.25 

4979 

2 

5.75 

4999.5 

05 

1.3 

3097 

91 

2.8 

4705 

22 

4.3 

4981 

2 

5.8 

4999.55 

05 

1.35 

3188 

87 

2.85 

4727 

21 

4.35 

4983 

2 

5.85 

4999.6 

05 

1.4 

3275 

85 

2.9 

4748 

19 

4.4 

4985 

2 

5.9 

4999.05 

05 

1.45 

3360 

2.95 

47G7 

4.45 

4987 

5.95 

4999.7 

36         Spelling  Ability — Its  Measurement  and  Distribution 

Thorndike  ('13,  p.  200),  presents  these  distances  in  units  of  P.E. 
By  reference  to  it  we  find  that  32.9%  corresponds  to  1.4088  P.E. 
In  a  similar  way,  the  6.1%  of  3d-grade  children  who  equal 
or  exceed  the  5th-grade  median  (Table  XIII)  serve  to  locate 
that  median  at  2.2929  P.E.  above  the  3d-grade  median.  The  6th- 
grade  median  is  3.0441  P.E.  and  the  7th,  3.6429  P.E.  above  the 
3d-grade  median.  The  distance  between  the  3d-  and  8th-grade 
medians  cannot  be  directly  calculated  owing  to  the  absence  of 
sufficient  overlapping. 


A 


1^: 


AJv      %*        ^<,'^t     '^^ 


Suppose  the  line  AB  to  represent  the  range  of  spelling  ability 
in  the  elementary  school.  At  a  certain  distance  above  A,  the 
absolute  zero-point,  stands  the  3d-grade  median,  M^.  Above  it 
and  at  distances  to  be  determined  are  the  medians  of  the  4th 

to  the  8th  grades,  M^ Mg.     For  brevity  we  shall  call  the 

distance  from  the  3d-  to  the  4th-grade  median  M..^,  etc.  M^^^ 
means  the  same  distance  as  M3.4,  but  measured  in  the  opposite 
or  negative  direction. 

TABLE  XV 
The  Per  Cent  of  Pupils  in  Each  Grade  Whose  Ability  Equalled 
OR  Exceeded  that  of  the  Median  Pupil  in  Every  Other 
Grade;  with  the  P.E.  Values  Correspond- 
ing TO  Each  Per  Cent 


3d 

4th 

5th 

6th 

7th 

8th 

Grade 

Grade 

Grade 

Grade 

Grade 

Grade 

3d  grade. . . . 

% 

17.1 

6.1 

2.0 

0.7 

0 

P.E. 

1 . 4088 

2.2929 

3.0441 

3.6429 

? 

4th  grade.  .  . 

% 

80.9 

31.3 

11.1 

5.8 

1.9 

P.E. 

—1.2962 

.7227 

1.8111 

2.3308 

3.0767 

5th  grade  . . 

% 

92.8 

71.8 

27.0 

14.2 

5.8 

P.E. 

—2.1663 

—  .8553 

.8819 

1 . 5888 

2.3308 

6th  grade.  . . 

% 

99.0 

91.9 

80.1 

34.0 

13.6 

P.E. 

—3.4500 

—2.0735 

— 1 . 2532 

.6117 

1.6291 

7th  grade  .  . 

% 

99.5 

96.4 

89.9 

70.1 

27.1 

P.E. 

—3.8200 

—2.6673 

—1.8918 

—  .7818 

.9041 

8th  grade   .  . 

% 

100 

99.6 

97.1 

87.0 

72.2 

P.E. 

■> 

—3.9375 

—2,8114 

— 1 . 6704 

—  .8730 

Location  of  Grade  Medians  3  7 

Table  XV  gives  all  the  distances  between  medians  which  our 
data  permit  us  to  calculate  directly.  The  P.E.  values,  reading 
across  the  table,  indicate  that  on  the  record  of  the  pupils  tested 
the  4th-grade  median  is  found  to  be  1.4088  P.E.  above  the  3d- 
grade  median,  the  5th  2.2929  P.E.  above  it,  the  6th  3.0441  P.E. 
above  it,  and  the  7th  3.6429  P.E.  above  it ;  that  the  3d-grade 
median  is  1.2962  P.E.  belozu  the  4th-grade  median,  the  5th  .7227 
P.E.  above  it,  etc. 

It  will  be  seen  that  M4  is  given  as  1.4088  above  M^,  while  M^ 
is  given  as  only  1.2962  below  M^.  We  shall  have  to  adopt  one 
or  the  other,  or  some  value  between  them  as  the  most  probably 
correct  distance,  il/3-4.  Similarly  for  each  of  the  other  distances 
(except  A/g-s)  vve  have  two  values,  and  these  two  values  are  in 
each  case  somewhat  different  one  from  the  other.  The  following 
are  the  pairs  of  values  which  Table  XV  shows: 


^3-4 

1.4088  and  1.2962 

^3-5 

2.2929 

" 

2.1663 

■^3-6 

3.0441 

a 

3.4500 

^3-7 

3.6429 

» 

3.8200 

^4-5 

.7227 

" 

.8553 

^4-8 

1.8111 

i( 

2.0735 

M,_, 

2.3308 

" 

2.6673 

^4-8 

3.0767 

<f 

3.9375 

^5-6 

.8819 

u 

1.2532 

^5-7 

1.5888 

" 

1.8918 

^5-8 

2.3308 

" 

2.8114 

^6-7 

.6117 

(( 

.7818 

■^6-8 

1.6291 

" 

1 . 6704 

M,_, 

.9041 

" 

.8730 

The  differences  between  these  pairs  of  values  is  in  most 
cases  small.  In  all  cases  they  afford  data  for  the  determination 
of  the  distances  between  medians  which  will  be  probably  more 
accurate  than  either  of  them. 

We  do  not,  however,  need  all  these  values.  If  we  have  five, 
namely,  Ms.^,  M4.5,  M^^,  M^.^,  and  M^.g,  all  the  others  may 
be  obtained  by  adding  these  together.  We  shall  therefore 
attempt  to  derive  as  accurately  as  possible  these  five  values  in 
temis  of  the  unit,  P.E.  Each  of  them  is  represented  directly  by 
two  quantities  as  shown  above.  But  it  is  clear  that  if  we  use 
more  of  the  data  of  Table  XV  we  may  obtain  values  whose 


38         spelling  Ability — Its  Measurement  and  Distribution 

accuracy  will  be  much  more  satisfactory.  We  may,  for  instance, 
find  for  the  distance  between  the  4th-grade  median  and  the 
5th-grade  median  (M^^g)  a  third  value  by  subtracting  from  the 
distance  between  the  3d-  and  5th-grade  medians  {M^^  =  2.2929) 
the  distance  between  the  3d-  and  4th-grade  medians  {M^.^^ 
1.4088).  This  gives  .8841.  Another  value  is  the  differeiice 
between  the  same  two  distances  expressed  negatively,  i.e.,  accord- 
ing to  our  notation,  between  M^.^  (2.1663)  ^"^  -^4-3  (1-2962;, 
which  is  .8701.  Again  we  may  use  the  difference  between  M^^ 
and  M^^,  between  M^^  and  M^^,  between  M^.^  and  M..^; 
and  for  each  of  these  differences  between  positive  quantities 
we  have  a  difference  between  corresponding  negative  quantities. 
This  adds  six  more  expressions,  making  ten  altogether,  for  the 
same  distance,  M^.^.  This  is  of  course  only  a  beginning  of  the 
great  number  of  combinations  which  may  be  used  to  get  expres- 
sions for  the  same  distance.  We  think  these  few,  however, 
since  they  use  each  of  the  18  segments  (nine  counted  both  ways) 
which  terminate  at  either  M^  or  M^  will  be  sufficient  to  determine 
M^.g  with  considerable  accuracy.  We  doubt  whether  the  remoter 
segments  (e.g.,  iWg.-,  Mg-g,  and  ikf^.g)  would,  if  used,  increase 
the  accuracy  at  all. 

Accordingly  we  have  calculated  10  values  for  M^.^,  M^^,  and 
ikfe-7-  Since  we  have  no  expression  of  direct  relation  between 
Mg  and  M^,  we  have  but  8  values  for  M^.^  and  M-.g.  Table 
XVI  gives  all  these  values  with  the  derivation  of  each.  It  also 
gives  the  averages,  unweighted  and  weighted,  of  the  values  for 
each  of  the  five  median  intervals. 

It  was  felt  that  to  give  each  of  these  items  the  same  weight 
was  to  fail  to  take  account  of  their  reliability.  The  direct  values 
are,  no  doubt,  most  to  be  depended  upon.  Those  computed  by 
using  a  distance  which  passes  over  one  median  are  less  so.  Those 
involving  two  or  more  of  these  "  skips  "  are  still  less  so  and 
diminish  in  reliability  as  the  number  of  "  skips  "  increases.  It 
will  be  found  that  in  column  2  of  Table  XVI  the  first  quantity 
.8841  is  derived  by  using  a  value  that  involves  one  skip.  M3.5 
skips  over  M.^,  while  M^.^,  which  is  taken  from  it,  presents  no 
skips.  The  second  quantity,  .7227,  is  direct,  and  there  are  no 
skips.  .9292  involves  one  skip,  .7420  three  skips  (M ^_-  skips  M^ 
and  Mg,  and  ilfj.^  skips  Mg),  etc.     It  will  be  found  upon  trial 


Location  of  Grade  Medians 


39 


TABLE  XVI 
Direct  and  Derived  Values  of  Median  Distances  in  Terms  of  P.E. 


■3A-/     .  oiit    .    f.ost    .  o.Cif ,    o.'iio  . 


At- 


A/*       fi-> 


Al, 


^^^3-. 

^^4-5 

5—0 

^^6-7 

M,_3 

1 . 4088 
(direct) 

.8841 

(M3_3-M3_,) 

.7512 

(M3_«-il/3_5) 

.5988 

(M3_3-M3_,) 

1 . 5704 

(M3_3-il/,_5) 

.7227 
(direct) 

1.0884 

(M,_6-M,_,) 

.5199 

.7459 
(M,_g-M,_,) 

1.2330 

.9292 
(M,_6-M5_e) 

.8819 
(direct) 

.7069 

.7420 

1.3121 

.7420 

(ilf,_,-M,_,) 

.9771 

(M,_-M,_,) 

.6117 
(direct) 

1.0174 

(Mg_8— Mg_7) 

(il/3-S-^^^4-8) 

.7459 
(M,_g-il/5_3) 

.7017 

(M5_8— Mg_8) 

.7250 

(Me_8-M,_s) 

.9041 
(direct) 

1.2962 
(direct) 

.8701 
(M5_3-M,_3) 

1.2837 

(M6_3— M5_3) 

.3700 

(M,_3-M,_3) 

(^^3-^^7-3) 

1.3110 

.8553 

(direct) 

1.2182 

.5938 
(M7_-Mg_,) 

1.2702 

1.3765 

.8203 
(M,_-Me_5) 

1.2532 
(direct) 

.6386 

.9196 
(Ms_5-M,_g) 

1.1527 

(il/,_3-3/,_,) 

.7755 

(iV/,_,-M,_5) 

1.1100 

.7818 
(direct) 

.8886 
(M3_g-M,_,) 

{M,_^-M,_,) 

1.1261 

(M,_,-M,_,) 

1.1410 

(Mg_5-Ms_,) 

.7974 

(M,_,-M3_,) 

.8730 

(direct) 

Average 

1.3326 

.8471 

1.0406 

.6344 

.9201 

Weighted 
Average 

1 . 3505 

.8363 

1.0505 

.6608 

.9101 

that  in  all  values  there  are  either  o,  i,  3,  or  5  skips.  We  have 
weighted  them  6,  4,  3,  and  2  respectively  (ratio  about  1.5). 
This  is,  of  course,  pure  assumption,  nor  do  we  know  of  any 
convenient  plan  of  weighting  which  would  not  be.     All  we  can 


40         Spelling  Ability — Its  Measurement  and  Distribution 

say  is  that  to  us  the  direct  values  seem  to  be  quite  one  and 
one-half  times  as  reliable  as  those  involving  a  distance  which 
passes  over  one  median,  that  it  seems  reasonable  the  latter 
should  be  about  as  many  times  more  reliable  than  those  involving 
3  skips,  and  that  the  derivation  with  5  skips  would  be  inferior 
in  approximately  the  same  ratio.  Weighting  therefore  as  above 
indicated,  we  obtain  values  for  the  median  distances  as  given  in 
the  last  line  of  Table  XVI.  These  are  the  measures  that  will 
be  used  in  this  study ;  but  they  dififer  so  little  from  those  obtained 
without  weighting  that  the  latter  may  serve  almost  as  well. 

Concretely  these  results  mean  that  if  we  represent  the  differ- 
ence between  no  spelling  ability  at  all  and  the  ability  of  typical 
3d-grade  children  by  x,  the  ability  of  typical  4th-grade  children 
will  be  represented  by  ;ir+i.35i,  of  typical  5th-grade  children 
by  X  +  1.35 1  +-836  or  x  +  2.187,  oi  typical  6th-grade  children  by 
X  +  3.238,  of  typical  7th-grade  children  by  x  +  3.899,  and  of 
typical  8th-grade  children  by  x  +  4.809.  (The  determination 
of  the  value  of  x  is  not  material  in  the  present  connection.  We 
shall,  however,  have  something  to  offer  on  this  point  in  a  later 
section.)  The  median  distances  suggest  that  so  far  as  spelling 
is  concerned  the  equal  time  intervals  of  one  year  between  the 
grades  do  not  at  all  correspond  to  the  differences  in  ability. 
The  difference  between  3d-grade  performance  and  4th-grade 
performance  is  more  than  twice  as  great  as  the  difference 
between  6th-  and  7th-grade  performance.  Whether  this  is  due 
to  a  more  or  less  common  failure  in  the  7th  grade  to  give  as 
much  attention  to  spelling  as  in  earlier  grades  or  whether  in 
general  6th  and  7th  grades  are  actually  closer  together  than 
others,  is  a  question  which  we  cannot  settle.  That  a  lack  of 
effort  to  instruct  in  spelling  in  the  higher  grades  does  not  fully 
account  for  the  differences  is  suggested  by  the  fact  that  the 
8th  grade  stands  at  a  greater  distance  from  the  7th  than  the  5th 
does  from  the  4th  or  the  7th  from  the  6th. 

§  12.    Scaling  the  Words 

Assuming  that  the  normal  surface  of  frequency  represents 
the  distribution  of  spelling  ability  in  each  grade,  we  shall  now 
seek  to  determine  how  difficult  each  one  of  the  50  words  listed 


Scaling  the  Words 


41 


in  Tables  III  and  IV  is  for  each  grade.  A  word  spelled  by  one 
hundred  per  cent  of  the  pupils  in,  say,  the  3d  grade  would  have 
no  difficulty  for  that  grade.  The  ability  of  all  pupils  would  be 
greater  than  the  ability  required  to  spell  it,  and  the  entire  area 
of  the  frequency  surface  would  lie  above  it — i.e.,  to  the  right  of 
it.  In  Fig.  12,  if  OP  represents  the  Probable  Error,  it  would  be 
located  theoretically  at  an  indefinite  distance  to  the  left  of  the 
point  0,  a  distance,  however,  which  we  may  for  practical  pur- 
poses call  5  or  6  times  as  great  as  OP — i.e.,  5  P.E.  or  6  P.E.  A 
word  spelled  by  98  per  cent  of  the  pupils  becomes  more  in- 
telligible. It  would  be  located  at  a  point  K,  a  vertical  at  which 
(KL)  would  cut  oflF  2  per  cent  of  the  area  of  the  entire  fre- 
quency surface.     The  point  K  will  be  found  to  be  at  a  distance 


Fig.  12.     Normal   Surface  of  Frequency. 

of  about  3  P.E.  below  the  median  O,  i.e.,  at  3  P.E.  A  word 
spelled  by  nobody — i.e.,  a  word  rated  at  o — would  be  at,  say, 
+  6  P.E.,  and  a  word  spelled  correctly  by  50  per  cent  of  the 
group  would  be  located  at  the  median  O,  that  is,  at  a  point 
above  and  below  which  are  an  equal  number  of  cases. 

It  will  be  interesting  and  will  serve  to  show  the  misleading 
character  of  per  cent  ratings  to  observe  what  we  mean  by 
saying  that  one  word  is  more  difficult  than  another.  Observe 
the  two  following  groups  of  words  taken  from  Tables  III  and  IV 
for  the  3d  grade: 


(A) 

Per  Cent 
Correct 

tailor 38 

lesson 37 

another 56 

wear 35 


(B) 

beautiful 

beginning 

telephone 

pigeons 


Per  Cent 
Correct 

10 
9 


42         spelling  Ability — Its  Measurement  and  Distribution 

According  to  the  ratings  of  these  words  the  differences  in 
point  of  difficulty  between  the  words  of  group  A  are  equal  to  the 
differences  in  group  B,  for  the  differences  are  all  represented 
by  I  per  cent.  Habitually  we  are  likely  to  think  that  this  is  true. 
But  such  a  way  of  thinking  quite  neglects  the  form  of  distribu- 
tion of  spelling  ability.  In  fact  it  assumes  that  the  frequency 
surface  is  a  rectangle — i.e.,  that  there  are  just  as  many  very 
poor  or  very  good  spellers  as  there  are  spellers  of  medium 
ability.  This  we  know  is  not  true.  The  mediocre  are  always 
much  more  numerous  than  the  dull  or  the  gifted.  A  figure  such 
as  Fig.  12  takes  account  of  this  fact. 

Now  the  words  in  group  A  are  much  nearer  the  median 
(which  would  be  a  word  50%  correct)  than  are  those  of  group 
B.  They  are  located  on  the  base  line  at  points  such  that  between 
adjacent  verticals  drawn  at  these  points  one  per  cent  of  the 
area  will  lie.  The  w^ords  of  group  B,  more  remotely  placed 
with  reference  to  the  median,  are  also  so  situated  that  between 
their  adjacent  verticals  one  per  cent  of  the  area  will  lie.  But 
the  points  for  group  B  stand  at  greater  distances  apart  than 
do  the  points  for  group  A  because  the  verticals  or  ordinates  are 
shorter  for  the  remoter  group.  As  a  matter  of  fact,  the  differ- 
ence in  difficulty  between  "  beautiful "  and  "  pigeons  "  is  more 
than  twice  as  much  as  the  difference  in  difficulty  between 
"  tailor  "  and  "  wear,"  although  each  difference  is  represented  by 
the  same  per  cent. 

Bearing  in  mind  the  meaning  of  these  per  cent  values  we  may 
readily  place  the  50  words  of  Tables  III  and  IV  along  the 
.ar-axis  or  base  line  of  a  normal  frequency  surface.  "  Even," 
which  is  rated  59  per  cent  for  the  3d  grade,  would  be  at  a  point 
below  the  median  between  whose  ordinate  and  the  median  ordin- 
ate is  9%  of  the  area  of  the  surface.  Calling  the  median  zero  and 
referring  to  Table  XIV,  we  find  that  9%  of  the  cases  (900  in 
10,000)  corresponds  to  a  value  of  P.E,  which  lies  between  .3 
and  .35.  By  interpolation  this  value  is  found  to  be  .338.  There- 
fore the  position  of  "  even  "  is  at  — .338  P.E.  This  may  be  repre- 
sented on  Fig.  13  by  the  point  i.  "  Lesson  "  (37%  correct)  will 
be  at  a  point  above  zero  between  which  and  zero  are  13%  of 
the  cases  of  a  normal  frequency  surface.  Table  XIV  locates 
this   point  at   +.49  P.E.    (Point   2,    Fig.    13).     "Only"    (65% 


Scaling  the  Words 


43 


correct)  is  at  — .572.P.E.  (Point  3,  Fig.  13)  ;  "  smoke"  (46%) 
at  +.148  P.E.  (point  4);  "pear"  (31%)  at  +.735  P.E.  (point 
5)  ;  "  minute  "  (26%)  at  +.955  P.E.  (point  6)  ;  "  cousin  "  (19%) 
at  +  1.300  P.E.  (point  7),  and  so  on.  Words  rated  above  50% 
are  located  below  the  median :  those  under  50%  are  above  the 
median.  Their  distances  from  the  median  are  negative  in  the 
first  case  and  positive  in  the  second. 

Assuming  the  same  form  of  distribution  for  the  4th  grade 
we  find  that  "  even  "  (79%)  is  located  at  —  1.20  P.E.,  "only  " 
(75%)  at  precisely  —  i.oo  P.E.,  and  "  pear  "  (42%)  at  +.30  P.E. 
Similarly  for  each  grade  by  using  the  per  cents  of  Table  III  and 
IV  and  the  P.E.  equivalents  of  Table  XIV  we  may  "  place  "  all 


^^ZP£.        P£.  3  I     H-  ZSieE,i    -fZlVE. 


Fig.    13.     Showing  the  placing  of   the  first   7  words   of   the   Preferred 

List.    3d  grade. 


the  words.  Table  XVII  gives  the  per  cents  and  P.E.  equivalents 
of  the  50  words  of  the  Preferred  Lists  which  from  now  on  will 
be  treated  as  one  list.  Figs.  14,  15,  16,  17,  18  and  19  show  how 
the  words  appear  when  arranged  on  a  linear  scale  for  each 
grade.  For  the  meanings  of  the  numbers,  each  of  which  refers 
to  a  word  of  the  Preferred  List,  see  Table  XVII  or  Appendix  II. 
Table  XVII  with  its  corresponding  figures  (14  to  19)  affords 
standards  for  grade  performances.  As  will  be  observed,  the  P.E. 
values  of  all  the  words  are  calculated  for  each  grade  with  refer- 
ence to  the  median  of  that  grade,  which  is  called  zero.  Their 
use  may  be  illustrated  with  reference  to  the  4th  grade.  We  may 
test  a  pupil  of  that  grade  by  beginning  with  the  easiest  word  and 
proceeding  to  the  next  hardest  and  the  next  and  so  on.  The 
series  would  run :  i  even,  3  only,  2  lesson,  or  5  front,  28  chicken, 
or  41  Tuesday,  4  smoke,  11  pretty,  8  bought.    ...    By  the  time 


44         Spelling  Ability — Its  Measurement  and  Distribution 


*0* 


•  ^5 


■  ?5 


(sS'f^ 


r"  "§; 

f^' 

p-l^ 

o 

+ 

o 

^ 

p- 


>o--'-> 


'<"o«wg 


-V)oo^ 


Scaling  the  Words 


45 


TABLE  XVII 

Per  Cents  Correct  and  P.E.  Equivalents  for  Each  Word  of  the 
Preferred  List.     Grades  3-8.     See  Figs.  14-19 


No. 

of 

Word 


1 
2 
3 

4 
5 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

36 
37 
38 
39 

40 

41 
42 
43 
44 
45 

46 

47 
48 
49 
50 


Words 


even . . 
lesson, 
only .  . 
smoke, 
front. . 


sure .  .  . 
pear  ... 
bought, 
another . 
forty. . . 


pretty. . 
wear.  .  . 
button . 
minute, 
cousin. . 


nails 

janitor . .  . 
saucer. . . . 
stopping. . 
sword. .  .  . 


freeze. .  . 
touch . .  . 
whistle. . 
carriage  . 
nor 


already. . . 
beginning, 
chicken. . . 
choose  .  .  . 
circus.  .  .  . 


grease. . 
pigeons, 
quarrel . 
saucy . . 
tailor .  . 


telegram., 
telephone, 
tobacco .  . 

too 

towel .... 


Tuesday. . 
tying .  .  .  . 
■whole.  .  .  . 

against. . . 
answer. .  . 


butcher .  . 
guess  .... 
instead. . . 

raise 

beautiful . 


3d  Year      4th  Year      5th  Year      6th  Year      7th  Year     8th  Year 


P.E. 


.337 
.492 
.571 
.149 
.037 

.112 
.735 
.376 
.531 
.037 


+  .187 
+  .571 
+  .693 
+  .954 
+  1.302 

+  .261 
+  1.302 
+  1.819 
+  .909 
+ 1 . 670 

+  .820 
+  .187 
+  1.145 
+  1.670 
—   .492 


+  1.475  42 
+ 1 . 98S  25 
+  .037  70 
+ 1 . 145 
+ 1 . 248 


+  1.819 
+  2.188 
+ 1 . 537 
+ 1 . 602 
+    .453 

+  1.537 
+2.083 

+  1.742 
+ 1 . 602 
+  1.047 


+    .149 
+    .224 
+  1.415 
+ 1 .  302  30 
.  909  47 


+  .652 
+ 1 . 248 
.693 
+  1.196 
+ 1 . 900 


P.E. 


—1.196 

—  .864 
—1.000 

—  .735 

—  .864 

—  .187 
+  .299 

—  .571 
+  .261 

—  .453 


.652 
.037 
.074 
.453 
.112 


—  .299  71 
+  .299  58 
+  .820  42 
+  .414|55 
+  .149:57 

+  .149;  68 

—  .074  60 


—  .187 
+  .376 

—  .414 

+  .299 
+  1.000 

—  .778 
+  .61 
+  .414 

+  1.3.57 

+  .820 

+  .414 

+  .571 

—  .187 


.735 
.571 
.414 
.864 
.224 

.778 
.299 
.261 
.778 
.112 

.337 
.693 
.074 
.149 
.074 


P.E. 


—1.819 
—1.415 
—1.819 
—1.537 
—1.248 

—  .735 

—  .299 
—1.196 
—1.145 

—  .571 

—1.047 

—  .414 

—  .414 

—  .453 

—  .735 

—  .820 

—  .299 
+    .299 

—  .187 
.261 

—  .693 

—  .376 
224 

!ooo 

—  .571 

+  .261 
+  .492 
—1.415 
+  .074 
.000 


+ 


.492 
.337 
.112 
.376 
.778 

.414 
.074 
.376 
.909 
.531 

.6.52 
.778 
.531 
.149 
.652 

.7.35 
.037 
.453 
.652 

.778 


P.E. 


—2.188 
-1.988 
—2 .  439 
—2 .  305 
— 1 . 900  94 


—1.145 

—  .864 
—1 .  988 
—1 .  602 

—  .864 

—1.900 

—  .954 

—  .909 
1.096 

—1.819 

1.670 
—1.302 

—  .299 

-  .820 
-1 .  145 

-1.415 
-1.302 

-  .531 

-  .652 

-  .693 

—  .453 
+  .149 
—1.900 

.376 

—  .864 

+    .571 

—  .261 
—1.000 

.074 
1.000 

—  .492 

—  .652 
—1.000 
+  1.047 

—  .909 

-1 .  248 

-  .693 
-1.145 
-1.000 
-1 .  602 

-1 .  537 

-  .652 
-1 .  602 
-1 .  475 
-1 .  537 


P.E. 


—2.188 
—2 .  305 
—2.789 
—2 .  597  99 
—2.305  97 


-1.819 
-1.302 
-2.305 
-2.305 
-1.415 

-1 . 900 
-1.475 
-  .954 
-1.602 
-1.819 

-2.083 
-1 .  302 
-1.196 
-1.047 
-1.602 


86  -1 .  602 

84  —1 .  475 

1.000 

81  — 1..302 

7—1.096 


+    .224 

—  .612 
—2 .  597 

—  .571 
—1.000 

+    .299 

—  .778 
— 1 . 602 

—  .820 
— 1 . 302 

—  .909 
—1.415 
— 1 . 742 
+  .778 
—1.145 

-1 .  670 
-1.047 
-1 .  475 
-1.475 
-1 .  f^OO 

-1.900 
-1.096 
-1 . 670 
-2.188 
-2.305 


P.E. 

—2.789 
—  2 .  597 
—3.450 
—3 .  450 
—2.789 

—2.305 
—2.305 
—2.789 
—2.597 
—1 .  670 

—2.305 
—2.188 
1.670 
—2 .  083 
—2.439 

—2.597 
—1 .  900 
1.302 
—1.475 
—2.188 

2.305 

—2.188 

1.537 

1.537 

—2.305 

1.096 

—1.000 

3 .  450 

1.357 

—2 .  439 

.261 

1.357 

—2.305 

—1.145 

—1.475 

—1.475 
1.670 
—2.597 
+  .261 
—2.305 

-1 .  988 
-1 .  670 
-1 . 900 
-2.305 
-2.789 

-2 .  789 
-1.537 
-1.988 
-2.. 305 
-2 .  597 


we  have  reached  13  button,  22  touch,  50  beautiful,  12  zvear,  and 
48  instead,  we  are  deaUng  with  a  group  of  words  which  50  per 
cent  of  4th-grade  children  spell  correctly.     The  performance  of 


46         Spelling  Abiluy — Its  Measurement  and  Distribution 

a  given  4th-grade  pupil  should  approximate  at  least  the  standard 
set  by  these  words.  If  we  are  asked,  "What  is  4th  grade  spelling 
ability?"  we  may  answer  that  it  is  the  ability  to  spell  these 
words  that  cluster  about  the  median.  Of  course  it  is  tO'  be 
expected  that  any  given  pupil  will  miss  some  of  the  easier  words 
and  spell  some  of  the  harder  words.  We  should  test  him  by  the 
whole  series  of  50  and  his  errors  for  words  below  the  median 
may  be  balanced  against  correct  spellings  of  words  above  the 
median  at  an  approximately  equal  distance.  He  may  miss 
49  raise  ( — .15  P.E.)  but  spell  20  sword  or  21  freeze  (+.15  P.E.). 
He  may  miss  16  nails,  but  spell  7  pear.  In  such  cases  he  should 
be  credited  with  having  spelled  the  easier  word. 

In  a  similar  way,  by  using  the  words  in  the  order  in  which  they 
are  placed  for  any  other  grade,  we  may  determine  whether  a 
child  is  as  good  a  speller  as  the  median  children  of  that  grade. 
We  do  not  need,  however,  to  use  the  median  as  a  standard  unless 
we  wish  to.  We  may  chodse  +  40  or  +  60  and  ascertain  whether 
children  are  able  to  spell  up  to  that  point  in  the  same  manner  as 
is  indicated  above  for  the  zero-point.  It  is  to  be  observed, 
however,  that  our  series  does  not  offer  a  very  satisfactory  test  in 
the  higher  grades  for  such  standards,  because  there  are  so  few 
words  that  are  placed  as  high  or  higher  than  +  40  or  -f  60. 
The  words,  in  short,  are  not  difficult  enough  for  this  purpose.  In 
a  later  section  of  the  paper  we  shall  introduce  harder  words  into 
the  series  precisely  with  the  object  of  affording  a  fuller  test  of 
ability  for  the  higher  grades. 

There  remains,  however,  for  the  present  one  other  use  which 
may  be  made  of  our  data.  We  may  wish  to  disregard  grades 
altogether  and  seek  an  answer  to  the  question,  In  general,  how 
hard  are  these  words  for  children  of  the  elementary  school  above 
the  2d  year?  or,  with  reference  to  a  graphical  representation, 
What  is  the  average  position  of  each  word  on  a  linear  scale — 
that  position  from  which  the  positions  for  each  grade  deviate 
by  the  smallest  amounts? 

To  answer  such  a  question  we  shall  have  to  use  one  point 
of  reference  for  all  grades  instead  of  a  different  one  for  each 
grade.  In  the  above  treatment  we  have  expressed  each  word- 
value  as  a  deviation  from  the  median  of  the  particular  grade 
we  were  considering.     We  shall  now  use  this  same  data  but 


Scaling  the  Words  47 

transfer  the  point  of  reference  to  the  third-grade  median  by 
using  the  median  intervals  which  were  derived  in  Section  11. 
In  Table  XVI  (page  39)  we  have  given  the  results  of  our  inquiry 
into  the  amounts  of  these  intervals  as  follows : 


From  Afg 

to  M^ 

1.351  P.E 

"      M, 

"  M, 

2.187     " 

"      M, 

"  M, 

3.238     " 

"      M, 

"  Mj 

3.899     " 

"      M^ 

"  Ah 

4.809     " 

Table  XVIII  gives,  for  each  of  the  50  words,  its  position  for 
each  grade  when  referred  to  the  3d-grade  median  as  the  zero- 
point  or  point  of  reference,  together  with  the  "  average 
position  "  of  each  word.  The  method  of  securing  these  figures 
may  be  illustrated  as  follows : 

From  Table  XVII  the  P.E,  values  of  the  word  "  even  "  for 
each    grade,    referred   to    its    own    median,    are    shown    to   be 


3d   grade, 

—  .337 

4th       " 

—1.196 

5th       " 

—1.819 

6th       " 

—2.188 

7th      " 

—2.188 

8th      " 

—2.789 

The  first  of  these  values  is  of  course  already  referred  to  the 
3d-grade  median.  To  refer  the  others  to  the  same  point  we  must 
increase  each  of  them  by  the  amount  by  which  each  grade 
median  stands  above  the  3d-grade  median,  i.e.,  we  must  find  the 
sum  (algebraic)  of  — 1.196  and  1.351,  of  — 1.819  and  2.187, 
of  — 2.188  and  3.238,  of  — 2.188  and  3.899,  and  of  — 2.789 
and  4.809.  These  sums  give  the  figures  of  Table  XVIII  for  the 
word  "  even."  Their  arithmetical  mean  is  taken  as  the  average 
position. 

Fig.  20  shows  the  averages  of  Table  XVIII  when  reduced 
to  a  scale.  The  noticeable  thing  about  these  tabular  and  graphic 
representations  is  the  fact  that  the  words  from  easiest  to  hardest 
differ  so  little.  The  words  "  even  "  and  "  only  "  (No.  i  and 
No.  3),  which  are  — .337  and  — .571  respectively  for  the  3d 
grade,  appear  above  the  zero  point  at  +.699  and  +.569. 
Similarly  the  word  "too"  (No.  39)  which  for  the  8th  grade 
alone  is  +  5.07  becomes  for  all  grades  only  +  3.491.    It  is  a  fact 


48        Spelling  Ability — Its  Measurement  and  Distribution 


TABLE  XVIII 

The  Position  of  Each  Word  in  Each  Grade  when  Referred  to  the  3d- 

Grade  Median  as  the  Zero-point;  and  the  Average  Position  of 

Each  Word  for  All  Grades,  when  so  Referred.     1=P.E. 


Word 

3d 

4th 

5th 

6th 

7th 

8th 

Avevr-  ge 

Num- 
ber 

Word 

Grade 

Grade 

Grade 

Grade 

Grade 

Grade 

Position 

1 

even 

—  .337 

.155 

.368 

1.050 

1.711 

2.020 

.699 

2 

lesson 

.492 

.487 

.772 

1,250 

1.594 

2.212 

1.135 

3 

only 

—.571 

.351 

.368 

.797 

1.110 

1.359 

.569 

4 

smoke 

.149 

.616 

.650 

.933 

1.302 

1.359 

.835 

5 

front 

—  .037 
.112 
.735 
.376 

.487 
1.164 
1.650 

.780 

.937 
1.452 

1.888 
.991 

1.338 
2.093 

2.374 
1.250 

1.594 
2.080 
2.597 
1.594 

2.020 
2.504 
2.504 
2.020 

1.057 

6 

sure    

1.568 

7 

pear 

1.958 

8 

bought 

1.169 

9 

another 

.531 

1.612 

1.042 

1.636 

1.594 

2.212 

1.078 

10 

forty 

.037 

.187 

.898 
.699 

1.616 
1.140 

2.374 
1.338 

2.484 
1.999 

3.139 
2.504 

1.758 

11 

pretty 

1.311 

12 

wear 

.571 
.693 

1.388 
1.277 

1 .  773 
1.733 

2.284 
2.329 

2.424 
2.945 

2.621 
3.139 

1.844 

13 

button 

2.026 

14 

minute 

.954 

1.804 

1.734 

2.142 

2.297 

2.726 

1.943 

15 

cousin 

1.302 

1.463 

1.452 

1.419 

2.080 

2.370 

1.681 

16 

nails 

.261 

1.052 

1.367 

1.568 

1.816 

2.212 

1.379 

17 

janitor 

1.302 

1.650 

1.888 

1.936 

2.597 

2.909 

2.047 

18 

saucer 

1.819 

2.171 

2.486 

2.939 

2.703 

3.507 

2.604 

19 

stopping 

.909 

1.765 

2.000 

2.418 

2.852 

3.334 

2.213 

20 

sword 

1.670 

2.500 

1.926 

2.093 

2.297 

2.621 

2.185 

21 

freeze 

.820 

1.500 

1.494 

1.823 

2.297 

2.504 

1.740 

22 

touch  

.187 

1.277 

1.811 

1.936 

2.424 

2.621 

1.709 

23 

whistle 

1.145 

1.164 

1.963 

2.707 

2.899 

3.272 

2.193 

24 

carriage 

1.670 

1.727 

2.187 

2.586 

2.597 

3.272 

2.340 

25 

nor 

—  .492 
1.475 

.937 
1.650 

1.616 

2.448 

2.545 

2.785 

2.803 
4.123 

2.504 
3.713 

1.652 

26 

already 

2.699 

27 

beginning 

1.988 

2.351 

2.679 

3.387 

3.287 

3.809 

2.917 

28 

chicken 

.037 

.573 

.772 

1 .  338 

1 .  302 

1.359 

.897 

29 

choose 

1.145 

1.963 

2.261 

2.862 

3.328 

3.452 

2.502 

30 

circus 

1.248 

1.765 

2.187 

2.374 

2.899 

2.370 

2.141 

31 

grease 

1.819 

2.708 

2.679 

3.809 

4.198 

4.548 

3.294 

32 

pigeons 

2.188 

2.171 

2.524 

2.977 

3.121 

3.452 

2.739 

33 

quarrel 

1 .  537 

1.765 

2.075 

2.238 

2.297 

2.504 

2,069 

34 

saucy  

1.602 

1.922 

2.563 

3.164 

3.079 

3.664 

2,666 

35 

tailor 

.453 

1.164 

1.409 

2.238 

2.597 

3.334 

1.866 

36 

telegram 

1.537 

2.086 

2.601 

2.746 

2.990 

3.334 

2.549 

37 

telephone 

2.083 

1.922 

2.261 

2.586 

2.485 

3.139 

2.413 

38 

tobacco  

1.742 

1.765 

1.811 

2.238 

2.157 

2.212 

1.988 

39 

too 

1.602 
1.047 

2.215 
1.575 

3.096 
1.656 

4.285 
2.329 

4.677 
2.754 

5.070 
2.504 

3.491 

40 

towel 

1.978 

41 

Tuesday 

.149 

.573 

1.535 

1.990 

2.229 

2.821 

1.550 

42 

tying 

.224 

1.052 

1.409 

2.545 

2.852 

3.139 

1.870 

43 

whole 

1.415 

1.612 

1.656 

2 .  093 

2 .  424 

2.909 

2.018 

44 

against 

1.302 

2.129 

2.038 

2 .  238 

2.424 

2.504 

2.106 

45 

answer 

.909 

1.463 

1 .  535 

1 .  036 

1.999 

2.020 

1.594 

46 

butcher 

.652 

1.014 

1 .  452 

1 .  701 

1.999 

2.020 

1.473 

47 

guess 

1.248 

2.044 

2.224 

2.580 

2.803 

3.272 

2.363 

48 

instead 

.693 

1.425 

1 .  734 

1 .  636 

2.229 

2.821 

1.756 

49 

rfiise     

1 .  196 
1 .  900 

1.202 

1 .  277 

1 .  535 

1  .  763 

1.711 
1.594 

2,504 
2.212 

1 .  652 

50 

beautiful 

I.409I   1.701 

1,682 

Scaling  the  Words 


49 


=? 


So   SP-S.S   fe'o   X   «   O   3 

=>  S,-^  bi)  c  3  ::  S  ^  « 


l:      o  »  &*  k^  , 


^  o 

«  bJO 


-    w   I.   tC  "<  rf          ^ 
S,rfcSs><UOOO 


icccororocococo'^ 


-O   3 


' 

T3 

u 

C 

^ 

rt 

C 

o 

rt 

"t: 

•o 

<u 

o 

H 

^ 

<u 

^ 

bO 

bC 

(B  rH3  rt       ^  3  S  2  2 
9^  3-3  ti  ^  ??  fcf)--   °  Sf 


&,p;  j2 


*^  a      o 

2  'ai  ^  ."3 

•9  5^  c 

G   O   2   c3 

3  o   3  .^ 


=3  o  2 

m   32   x 


1— ((NCC-^iOOt^OCOTO 


S   g   >>0    3    P 


CO  ^' 
1^   O 


Ol 


-3    ?5 
,   bC":3   >i 
3   Otf 


O  i-i  N  CO  •*  "5  O  l^  00  Oi  O 

3-^ 


fe 


50        Spelling  Ability — Its  Measurement  and  Distribution 

then  that  for  these  ivords  the  influence  of  higher  grades  is  to 
make  easy  words  harder  and  of  lower  grades  to  make  hard 
words  easier.  That  is,  grade  considered,  these  words  are  harder 
for  children  of  the  upper  grades  than  they  are  for  those  of 
the  lower  grades.  There  are  at  least  two  reasons  for  this 
condition. 

First,  as  a  rule  these  particular  words  are  taught  in  the 
lower  grades.  A  popular  speller,  taken  at  random,  presents 
31  of  the  50  words  in  the  3d  year's  work,  10  in  the  4th,  2  in 
the  5th,  and  none  in  higher  grades.  There  is  nothing  to  lead 
one  to  suppose  that  this  is  peculiar.  The  words  were  among 
those  chosen,  it  will  be  remembered,  as  at  least  in  the  speaking 
vocabulary  of  3d-grade  children.  Most  of  them  if  taught  at  all 
will  be  taught  in  that  grade.  We  may  assume  therefore  that 
the  3d-grade  record  is  somewhat  affected  by  the  recency  with 
which  these  words  have  been  presented.  The  succeeding  grades 
will  to  some  extent  be  discriminated  against  in  the  record. 

Second,  the  necessary  basis  of  selection  for  these  words  from 
the  larger  lists  would  make  it  impossible  for  the  words  to  take 
the  same  position  on  the  scale  for  all  grades.  Consider  a  word 
which  was  spelled  correctly  by  50%  of  the  3d-grade  children. 
Such  a  word  would  be  at  M^.  In  order  to  take  the  same  position 
on  the  8th-grade  record  it  must  be  as  far  below  M^  as  is  the 
distance,  already  determined,  between  M^  and  Mg  or  — 4.809 
P.E.  To  do  this  it  would  have  to  be  spelled  correctly  by  9994 
pupils  out  of  10,000  (Table  XIV),  i.e.,  it  would  be  100%  correct. 
But  such  a  word  would  not  have  been  selected,  because  it  is  not 
difficult  enough  in  the  8th  grade  to  be  of  any  value  as  a  test  of 
ability.  On  the  other  hand,  a  word  missed  often  enough  in  the 
8th  grade  to  be  satisfactory  as  a  test  (say,  90%  correct)  would 
have  to  be  less  than  i  %  correct  on  the  3d-grade  record  in  order 
to  take  the  same  position  on  the  scale.  Such  a  word  would  have 
been  of  no  use  as  testing  3d-grade  ability  and  would  have  been 
rejected. 

The  fact  is  that  the  span  from  3d  to  8th  grade  is — if  our  median 
distances  be  correct — too  great  for  any  list  of  words  to  be  in  all 
respects  satisfactory.  We  need  several  lists  each  of  which  shall 
be  given  to  three  or  four  consecutive  grades  and  overlapping 
on  one  another — e.g.,  one  for  2d,  3d,  and  4th  grades,  another 


The  Use  of  the  Scale 


51 


for  3d,  4th,  5th  and  6th  grades,  and  another  for  5th,  6th,  7th 
and  8th  grades.  An  attempt  will  be  made  in  a  later  section  to 
do  this  and  to  show  the  results  that  may  be  expected. 

§  13.     The  Use  of  the  Scale 
Meanwhile,  however,  we  venture  to  think  that  the  scale  as 
^hown  in  Fig.  20  is  important  and  valid  within  its  range.     It 
may   be    used   in    several    ways   of    which    at   least   three    are 
important. 

1.  It  may  be  used  just  as  it  is  without  reference  to  the  fact 
that  the  words  are  not  separated  from  each  other  by  equal 
intervals.  We  know  the  value  or  weight  to  assign  to  each  word. 
We  shall  therefore  not  make  the  mistake  of  assuming  that  all 
the  words  are  of  the  same  value,  as  is  the  usual  school  practice. 

2.  Certain  words  of  the  series  may  be  used  which  differ  from 
each  other  by  approximately  equal  steps. 

TABLE  XIX 

Words  Arranged  in  Order  op  Difficulty  According  to  the  Scale 

AND  Their  P.E.  Values 


No.  on 
Scale 


3 

1 

4 

28 

5 

9 

2 

8 

11 

16 

46 

41 

6 

45 

25 

49 

15 

50 

22 

21 

10 

48 

12 

35 

42 


Word 

only 

even 

smoke. . . . 
chicken .  . 

front 

another .  . 
lesson.  .  . . 
bought. .  . 

pretty 

nails 

butcher.  . 
Tuesday. . 

sure 

answer.  . . 

nor 

raise 

cousin 

beautiful . 
touch  . . . . 
freeze. . . . 

forty 

instead. . , 

wear 

tailor.  .  . . 
tying .  .  . 


P.E.  X  100 


57 
70 
84 
90 
106 
108 
114 
117 
131 
138 
147 
155 
157 
159 
165 
165 
168 
168 
171 
174 
176 
176 
184 
187 
187 


No.  on 
Scale 


14 
7 
40 
38 
43 
13 
17 
33 
44 
30 
20 
23 
19 
24 
47 
37 
29 
36 
18 
34 
26 
32 
27 
31 
39 


Word 

minute. . . 

pear 

towel .  .  . . 
tobacco  .  . 
whole.  . . . 
button . . . 
janitor . . . 
quarrel. . . 
against . . . 
circus.  .  .  . 
sword.  .  .  . 
whistle.  .  . 
stopping . 
carriage . . 
guess  .  .  .  . 
telephone, 
choose . .  . 
telegram . 

saucer 

saucy  . . . . 
already. . . 
pigeons. . , 
beginning 
grease. . .  . 
too 


P.E.  X  100 


194 
196 
198 
199 
202 
203 
205 
207 
211 
214 
219 
219 
221 
234 
236 
241 
250 
255 
260 
267 
270 
274 
292 
329 
349 


52         spelling  Ability — Its  Measurement  and  Distribution 


3.  Small  groups  of  words  may  be  so  selected  as  to  be 
equally  difficult  as  groups ;  or  they  may  be  so  selected  that  their 
group-difficulties  constitute  an  ascending  series  from  easy  to 
hard,  differing  by  equal  amounts. 

1.  By  the  first  of  these  methods  the  entire  series  would  be 
utilized  or  so  much  of  it  as  in  any  given  case  would  thoroughly 
test  the  subject.  The  order  of  the  words  of  the  series  as  given 
in  Figure  20  is  shown  in  Table  XIX  in  the  first  column  and  in 
the  second  column  the  test  values  or  weights  of  these  words 
are  given. 

2,  If  it  is  desired  to  use  a  scale  whose  words  differ  in 
difficulty  by  equal  steps,  the  arrangement  as  shown  in  Table 
XX  will  be  found  convenient. 

TABLE  XX 
A  Ten-point  Scale 


No.  of 

Word 

(Fig.  20) 


Word 


P.E.  X  100 


3 
4 
9 
11 
45 
35 
30 
37 
34 
27 


only 

smoke. . . . 
another . . 

pretty 

answer.  .  . 
tailor.  .  . . 
circus .... 
telephone, 
saucy .... 
beginning. 


57 
84 
108 
131 
159 
187 
214 
241 
267 
292 


27 
24 
23 
28 
28 
27 
27 
26 
25 


To  this  series  may  be  added  39  "  too  "  whose  P.E.  x  100  is 
349  and  which  differs  from  "  beginning  "  by  57  or  approximately 
two  steps. 

In  the  series  of  Table  XX  the  average  step  is  26.2  with  an 
A.D.  of  1.3;  or  if  the  word  "too"  is  included  the  average  step 
is  26.6  with  an  A.D.  of  1.4.  This  is  quite  accurate  enough  for 
any  use  to  which  the  scale  is  likely  to  be  put.     If  this  conclusion 


The  Use  of  the  Scale  53 

is  accepted,  these  eleven  words  may  be  used  to  express  our 
judgments  of  other  words  concretely  and  in  terms  that  every- 
body can  understand.  We  should  not  then  have  to  resort  to 
such  terms  as  "  hard,"  "  easy,"  "  rather  difficult,"  "  very  hard," 
etc.,  but  we  may  judge  a  word  to  be  "  as  hard  as  '  another,'  " 
"  equal  in  difficulty  to  '  beginning,'  "  "  as  hard  as  '  answer  '  but 
not  as  hard  as  '  tailor,'  "  etc.  It  is  very  desirable  that  other 
words  should  at  some  time  be  added  to  the  scale  at  both  ends. 
There  are  many  words  harder  than  "  beginning  "  or  "  too  "  and 
there  are  others  easier  than  "  only,"  although  the  latter  do  not 
constitute  much  of  a  school  problem.  Neither  set,  however, 
could  be  used  over  a  range  as  wide  as  3d  to  8th  grades. 

3  (a).  It  is  often  desirable  to  offer  tests  of  equal  difficulty, 
but  of  different  words  at  various  intervals  of  time  to  the  same 
group  or  to  the  same  individual.  We  may  thus  secure  a  progress 
record.  In  spelling,  however,  this  has  proved  to  be  very  difficult 
if  not  impossible.  We  can  never  be  sure  that  the  second  or 
third  test  is  equal  in  difficulty  to  the  first  test.  In  fact  we  may 
be  pretty  sure  it  is  not.  To  give  the  same  words  over  again  is 
often  valueless  because  of  the  added  special  familiarity  with 
them.  The  following  lists  therefore  are  offered  as  lists  of  equal 
difficulty.  The  sum  of  the  P.E.  values  in  each  is  976  or  977.  In 
using  them  the  words  may  be  weighted  as  indicated,  or  may,  with 
no  great  loss  in  precision,  be  each  given  a  credit  of  i. 

Number  _  Number 

in  Preferred  in  Preferred 

List  Weight  List  Weight 

Group  A  Group  B 

41  Tuesday 16  45  answer 16 

10  forty 18  48  instead 18 

40  towel 20  43  whole 21 

44  against 22  17  janitor 21 

47  guess 24  24  carriage 24 

Group  C  Group  D 

49         raise 17  21  freeze 18 

22        touch 17  12  wear 19 

42  tying 19  7  pear 20 

14  minute 20  13         button 21 

18         saucer 27  20         sword 22 

Group  E  Group  F 

16         nails 14  S  bought 12 

46        butcher 15  11  pretty 13 

15  cousin 17  19  stopping 23 

29         choose 26  37  telephone 25 

32         pigeons 28  34  saucy 27 


54         spelling  Ability — Its  Measurement  and  Distribution 


(b)  It  may  also  be  desirable  to  test,  not  with  single  words, 
which  only  in  the  long  run  may  be  expected  to  conform  to  the 
positions  assigned  to  them,  but  with  groups  of  words  whose 
difficulties  as  groups  differ  by  constant  amounts.  Such  a  series 
of  groups  arranged  from  easy  to  hard  would  themselves  con- 
stitute a  scale — a  sort  of  Binet-Simon  scale  for  measuring  ability 
in  spelling.  On  the  analogy  of  the  Binet-Simon  scale  we  might 
easily  fix  upon  a  certain  minimum  performance  for  a  group  at 
which  or  better  than  which  a  subject  might  be  allowed  to  have 
"  cleared  "  that  group  and  might  pass  on  to  the  next.  He  might 
also  be  given  additional  credits  for  spelling  words  in  groups 
above  the  highest  one  which  he  cleared. 

The  groups  are  arranged  in  order  of  difficulty,  Group  I  being 
the  easiest  and  Group  VII  the  hardest.  Within  each  group  the 
four  words  are  also  arranged  in  their  order  of  difficulty  begin- 
ning with  the  easiest.  Since,  however,  within  each  group  the 
words  differ  little  in  difficulty,  they  may  be  taken  as  having 
equal  weights  without  material  error.  It  is  true  that  Group  VII 
is  not  nearly  as  satisfactory  in  this  respect  as  the  others,  differing 
between  the  first  and  fourth  words  by  1.08  P.E.,  whereas  the  first 
six  groups  have  a  range  of  but  .225  on  the  average. 

Group  I                     P.E.  X  100                 Group  IV 
3     only 57  10     forty 


1     even. . .  , 

4     smoke . 

28     chicken 


70 
84 
90 


12     wear. 
42     tying .  . 
38     tobacco 


Average. 


Group  II 
5  front .  .  .  . 
9  another . . 
2  lesson. . .  . 
8     bought . . . 


Average. 
Group  III 

16    nails 

46     butcher 

41     Tuesday  .  .  .  . 
6     sure 


75 
P.E.  X  100 
106 
108 
114 
117 

111 
P.E.  X  100 
138 
147 
155 
157 


Average. 
Group  V 

33     quarrel 

30     circus 

24     carriage 

47     guess 


29 
36 
34 
26 


Average. 
Group  VI 

choose 

telegram  .  .  .  . 

saucy 

already 


Average . 


149 
Group  VII 
37  telephone . 
32  pigeons  .  .  . 
31  grease  . .  .  . 
39     too 


Average. 
P.E.  X  100 
241 
274 
329 
349 


P.E.  X  100 

176 

184 

187 

199 

186.5 
P.E.  X  100 
207 
214 
234 
2.36 

223 
P.E.  X  100 
250 
255 
267 
270 

260.5 


Average . 


298 


The  Zero  Point  of  Spelling  Ability  55 

The  average  differences  in  difficulty  between  these  groups  in 
succession  are  36,  38,  37.5,  36.5,  37.5  and  37.5.  This  is  probably 
the  most  important  use  of  the  scale,  for  present  school  practice. 

If  it  is  true  that  the  general  scale  (Table  XVIII  and  Fig.  20) 
may  be  used  in  these  three  ways — as  a  whole,  by  words  selected 
to  be  at  equal  intervals,  and  by  grouping  words  so  that  the  groups 
are  equal  or  differ  by  equal  amounts — then  it  is  also  true  that 
each  of  the  grade  scales  (Figs.  14-19)  may  be  used  in  like 
manner  each  for  the  grade  to  which  it  applies.  It  is  probably 
true,  moreover,  that  the  grade  scales  will  more  closely  fit  real 
conditions  in  any  given  instance  than  will  the  scale  for  all  grades. 
The  labor  of  making  selections  and  groupings  of  words  for 
these  scales  is  not  great  and  may  be  made  by  any  one  on  the 
analog}'  of  the  method  used  above. 

§  14.     The  Zero-Point  of  Spelling  Ability 

As  has  been  suggested  in  previous  sections,  we  have  only  suc- 
ceeded in  scaling  by  means  of  these  50  words  a  limited  segment 
of  the  entire  projection  representing  spelling  ability.  Our  list  is 
essentially  an  easy  list,  testing  that  abilit>'  only  to  a  moderate 
degree.  Words  like  "  fatiguing,"  "  guarantee,"  and  "  conscien- 
tious "  (Rice  Sentence  Test)  would  stand  much  higher  in  the 
scale  and  require  a  considerable  extension  of  it  to  the  right; 
while  such  unfamiliar  words  as  "  eurycerous,"  "  delitescence," 
and  "gallinaceous"  (Klein,  '12,  pp,  388,  389)  would  take  still 
higher  positions,  passing  quite  beyond  the  range  of  the  ability  of 
elementary-school  children. 

On  the  other  hand,  our  scale  is  as  certainly  limited  at  the  low 
end.  There  are  many  easier  words  than  any  we  have  used  so  far. 
Such  words  would  reach  far  down  on  the  scale  towards  the  place 
where  the  absolute  zero-point  lies.  But  they  would  have  been 
totally  unfit  for  use  in  the  higher  grades.  In  fact,  with  the  wide 
range  of  ability  between  3d  and  8th  grades,  it  is  surprising  that 
we  find  any  words  at  all  which  will  afford  a  test  at  both 
extremes. 

Without  seeking  to  determine  the  limit  of  the  high  end  of 
the  scale — perfect  spelling  ability — it  is  quite  possible,  and 
theoreticallv  verv  desirable,  to  find  the  limit  of  the  low  end,  i.e.. 


56         Spelling  Ability — Its  Measurement  and  Distribution 

to  find  the  point  where  spelling  ability  just  begins  to  be  a  positive 
quantity. 

How  far,  then,  below  the  3d-grade  median,  which  has  hitherto 
been  our  point  of  reference,  is  the  absolute  zero-point? 

In  order  to  answer  this  question,  a  test  was  given  to  children 
of  the  2d,  3d,  and  4th  grades.  It  consisted  of  50  words  in 
sentences.  Nineteen  of  these  had  already  been  used  in  the 
Selected  List  (100  word  list)  ;  and,  of  these,  6  had  been  chosen 
for  the  Preferred  List.  They  had  all  been  spelled,  about  40  per 
cent  or  more  correct,  by  the  third-grade  children.  The  remain- 
ing 32  words  were  thought  to  be  among  the  easiest  in  the 
language:  he,  is,  on,  the,  to,  of,  for,  day,  etc. 

They  were  put  into  sentences  as  follows  and  dictated  at 
schools  II  and  VIII: 


Easy  50- Word  Test 

You  will  hear  him  coming. 

He  is  on  the  road  and  is  almost  sure  to  pass  in  front  of  me. 

I  send  for  him  every  day. 

Go  into  the  school. 

But  do  not  touch  the  table. 

He  also  has  only  one  pair  of  shoes. 

They  are  not  at  all  pretty. 

No  man  ought  to  steal  even  a  penny. 


It  seems  clear  that  a  child  who  cannot  spell  any  one  of  these 
words  has  substantially  no  spelling  ability.  Since  our  study  is 
limited  to  written  words  we  shall  say,  therefore,  that  for  our 
purpose  a  child  who  does  not,  save  by  chance,  write  a  single 
word  of  this  list  so  that  it  can  be  recognized  as  correctly  spelled 
has  no  ability. 

On  account  of  the  marked  improvement  in  spelling  of  children 
in  the  latter  half  of  the  second  school  year  over  those  in  the 
first  half  of  that  year,  we  have  treated  the  two  half-years  of 
the  2d  grade  separately,  calling  the  lower  half  2a  and  the  upper 
2b.  We  shall  proceed  as  follows.  We  shall  find  the  distance 
between  the  3d-grade  median  and  the  2&-grade  median  and  the 
distance  between  the  latter  and  the  2a-grade  median.  Then  if 
there  are  children  of  the  2a  grade  who  utterly  break  down  and 


The  Zero  Point  of  Spelling  Ability 


57 


fail  to  write  any  word  correctly  we  shall  find  their  place  in  the 
2a  distribution. 

Table  XXI  shows  the  records  of  individual  pupils  according 
to  their  rating  in  the  Easy  50-Word  Test.  Note  the  fact  that 
no  children  of  the  4th,  3d,  or  2b  grades  wholly  failed  in  this 
test.  In  2a,  however,  39  children  were  rated  10%  or  less,  and 
of  these  there  were  8  pupils  who  were  actually  marked  zero. 
This  is  4.6%  of  all  the  children  of  2a. 


TABLE  XXI 
Distribution  of  Individual  Ratings.     Easy  50-word  Test 
Table  reads:    in  2a  39  children,  or  22%,  were  rated  between  0  and  10%; 
32  children,  or  18%,  were  rated  between  11%  and  20%,  etc.     In  26  5  chil- 
dren, or  3%,  were  rated  between  11%  and  20%,  etc. 


Per  Cent  Correct 

2(7  Grade 

26  Grade 

3d  Grade 

4th  Grade 

No. 

% 

No. 

% 

No. 

% 

No. 

% 

0-  10 

39 

32 

37 

27 

18 

14 

5 

2 

1 

0 

22 
18 
21 
16 
10 
18 

3 

1 
.6 

0 

0 
5 

9 
29 
26 
47 
31 
14 
7 
1 

0 

3 

5 
17 
15 
28 
18 

8 

4 
.6 

0 

1 

4 

7 

11 

25 

33 

36 

30 

21 

0 
.6 

2 

4 

7 
15 
20 
21 
18 
13 

0 
0 
0 
0 

4 
13 
29 
50 
86 
134 

0 

11-  20 

0 

21-  30 

0 

31-  40 

0 

41-  50 

1 

51-  60 

4 

61-  70 

9 

71-  80 

16 

81-  90 

27 

91-100 

42 

Totals 

175 

169 

168 

316 

Medians 

26.50 

56.17 

72.50 

88.12 

The  medians  for  the  grades  are  as  follows :  for  2a,  26.50% ; 
for  2b,  56.17%;  for  3d  grade,  72.50%;  and  for  4th  grade, 
88.12%.  The  rapid  rise  of  spelling  ability  from  low  second 
through  the  fourth  grade  is  remarkable.  It  is  much  greater 
than  the  improvement  during  the  next  four  years.  Although 
the  interval  in  time  between  2a  and  2&  is  but  half  a  year,  the 
medians  suggest  that  the  increase  in  ability  between  these  grades 
is  greater  than  it  is  between  any  consecutive  yearly  grades  above 
the  second.  Further  analysis  will  more  precisely  confirm  this 
inference. 

Proceeding  as  in  the  case  of  grades  3  to  8,  we  show  in 
Table  XXII  the  amount  and  per  cent  of  overlapping  of  each 


58         Spelling  Ability — Its  Measurement  and  Distribution 


grade  beyond  the  medians  of  the  other  grades,  together  with 
the  corresponding  linear  segment  in  terms  of  the  Probable  Error 
as  a  unit. 

TABLE  XXII 

Amount  and  Per  Cent  of  Overlapping  with  P.E.  Equivalents. 
I  Easy  50-word  Test 


2a  Grade 


2h  Grade 


3d  Grade 


4th  Grade 


2a  grade. 
26  grade. 
3d  grade. 
4th  grade 


No. 

% 
P.E. 

No. 

% 
P.E. 

No. 

% 
P.E. 

No. 

% 
P.E. 


160 
94.67 
2 . 3932 

165 
98.21 
3.1143 

316 

100 

? 


17 

9.71 

1.9254 


140 
83.33 
1 . 4341 

308 
97.47 
2.8976 


3 

1.71 

3.1429 

22 

13.02 
1 . 6690 


262 
82.91 
1 . 4094 


0 
0 
? 

4 

2.37 

2.9395 

30 

17.86 
1 . 3649 


From  these  results,  Table  XXIII  is  computed.  The  object  in 
this  table  is  to  show  how,  by  using  all  the  data  of  Table  XXII, 
various  values  of  the  median  intervals  may  be  obtained  whose 
averages  will  be  the  most  probably  correct  values.  The  interval 
between  the  medians  of  2a  and  2b  is  written  M2a-2b;  that 
between  the  medians  of  2b  and  the  3d  grade  is  written  M2&-3  ;  etc. 

It  may  be  remarked  parenthetically  that  in  the  number  1.3771 
of  Table  XXIII  for  the  difference  between  the  3d-  and  4th- 
grade  medians,  we  have  a  striking  confirmation  of  the  substan- 
tial accuracy  of  our  results  as  shown  in  Table  XVI.  The 
corresponding  number  is  there  given  as  1.3505.  That  these  should 
differ  by  so  little  when  carried  out  upon  different  test  material 
is   exceedingly   satisfactory. 

According  to  Table  XXIII,  the  2&-grade  median  is  approxi- 
mately 1.35  P.E.  below  the  3d-grade  median.  The  2a-grade 
median  is  about  1.87  P.E.  further  below,  or  3.22  P.E.  below  the 
3d-grade  median  which  we  have  thus  far  used  as  our  origin  or 
point  of  reference. 

But  we  have  not  yet  reached  the  point  of  zero  ability.    Typical 


The  Zero  Point  of  Spelling  Ability  59 

TABLE  XXIII 

Values  of  Median  Intervals  and  Their  Derivation 
(2a-4TH  Grade) 


^-^20-26 

^hh-z 

^3-4 

1 . 9254 
(direct) 

1.6690 
(direct) 

1.3649 
(direct) 

2.3932 
(direct) 

1.4341 
(direct) 

1.4094 
(direct) 

1 . 4739 
(^20-3— -^-''2&-3) 

1  2175 

(^20-3—^^20-26) 

1 . 2705 

(^-^26-4—^^26-3) 

1.6802 
(^3a-2— ^^^3-26) 

1.5746 
.7211 

(^3-2a— ^1^26-2a) 

1.4882 
(^4-26—^4-3) 

1 . 4635 

(^4-26— -'^^3-26) 

Averages    1 .  8682 

1.3518 

1.3771 

2a  children  have  some  ability,  namely,  according  to  our  record, 
an  ability  to  score  26.5%  in  the  Easy  50-Word  Test.  The 
children  of  that  grade  who  were  unable  to  write  any  word 
correctly  were  8  in  number,  representing  4.6  per  cent.  These  8 
are  included  in  the  39  rated  between  zero  and  10%  (Table 
XXI).  Assuming  that  2a  children  are  grouped  about  their 
median  according  to  the  "  normal "  distribution,  we  find  that 
in  order  to  cut  off  4.6%!  from  the  low  end  we  must  take  a  point 
2.5  P.E.  below  the  median,  (See  Table  XIV).  This  brings  the 
zero-point  at  5.72  P.E.  below  the  3d-grade  median  (3.22  +  2.5). 
This  figure,  5.72  P.E.,  can  only  be  taken  as  approximately 
correct.  It  would  be  somewhat  influenced  by  an  increase  of  the 
number  of  children  tested.  There  is,  however,  no  reason  to 
suppose  that  the  children  i-^  schools  II  and  VIII  were  unusual. 
The  testing  in  grades  3  to  8  in  all  other  schools  shows  that 
results  in  these  two  schools  do  not  materially  differ  from  the 
general  results.  In  both  central  tendencies  and  variabilities  they 
are  a  fair  average.  There  seems,  then,  to  be  no  good  reason 
why  we  should  not  consider  the  ratings  of  children  in  these 


6o         Spelling  Ability — Its  Measurement  and  Distribution 

schools  as  typical.  It  must  be  borne  in  mind,  however,  that  the 
classification  of  children  into  grades  is  a  broad  one.  Just  as  we 
found  it  necessary  to  treat  2d-year  children  in  half-yearly 
sections,  so  we  should  find  that  testing  at  the  beginning  even 
of  a  20-week  term  would  yield  results,  especially  in  the  low 
grades,  quite  different  from  those  obtained  by  testing  toward 
the  close  of  the  term.  Accordingly,  the  middle  of  the  term  is 
the  best  time  at  which  to  find  typical  conditions.  Moreover, 
in  order  that  the  results  may  be  comparable,  the  testing  of  all 
grades  should  be  done  at  the  same  time.  If  2a  children  were 
tested  towards  the  end  of  their  term  in  that  grade,  while  2& 
children  were  tested  towards  the  beginning  of  theirs,  the  median 
interval  would  be  unduly  shortened.  A  considerable  addition 
to  the  reliability  of  our  results  is  found  in  the  fact  that  all 
children  were  tested  during  the  loth  week  of  a  20-week  term. 

We  may  therefore  conclude  that  the  intervals  between  grades 
2a,  2b,  3  and  4  are  substantially  as  found  in  Table  XXIII.  But 
as  to  the  distance  of  the  zero-point  below  the  2a-grade  median, 
we  cannot  be  precise.  Four  and  six-tenths  per  cent  of  the 
2a  children  got  no  word  right.  As  many  as  22  per  cent  wrote 
less  than  6  words  correctly.  Some  of  them  probably  spelled 
these  few  simple  words  correctly  by  mere  chance.  If  this  were 
true,  they  would  have  practically  no  spelling  ability.  The 
situation  is  more  complicated  than  the  above  analysis  indicates. 
If  we  were  to  assume  that  all  the  children  who  wrote  0-5  words 
correctly  had  practically  no  spelling  ability  (written),  the  zero- 
point  would  then  be  but  1.15  P.E.  below  the  median  instead 
of  2.5  P.E.  If  we  were  to  assume  that  some  of  these  children — 
say  those  who  wrote  no  more  than  3  words  correctly — had  zero 
ability,  we  should  find  that  29  of  the  39  in  Table  XXI  were 
included.  Such  an  assumption  would  place  our  zero-point  at 
1.44  below  the  median.  There  are  reasons  for  thinking  that 
this  is  not  far  from  the  true  position.  The  best  judgment,  there- 
fore, that  we  can  make  from  our  data  and  from  our  knowledge 
and  experience  of  school  conditions  is,  that  the  zero-point  is 
about  1.5  P.E.  below  the  2a  median,  or  about  4.72  P.E.  below 
the  3d-grade  median. 

We  may  summarize  our  results,  then,  in  Table  XXIV  and 
Fig.  21,  as  follows: 


Observations  on  the  Distributions  Shown  in  Fig.  21  61 

TABLE  XXIV 
Median  Intehvals.     Zero  to  8th  Grade  Medl\n 


Successive 
Intervals 

Distance 
Above  0 

2a    grade 

26        "      

1.50 

1.87 

1.35 

1.35 

.84 

1.05 

.66 

.91 

1.50 
3.37 

3d        "      

4.72 

4th      "     

6.07 

5th      "     

6.91 

6th      "     

7.96 

7th      "     

8.62 

8th      "     

9.53 

Fig.  21,  page  62,  shows  these  facts  graphically. 

§   15.     Observations  on  the  Distributions  Shozvn  in  Fig.  21 

It  is  to  be  remembered  that  in  Fig.  21  the  eight  surfaces  of 
frequency  constructed  on  each  median  vertical  are  theoretical 
and  not  according  to  the  record.  ^Moreover,  they  express  the 
assumptions  that  for  each  grade  the  distribution  of  ability  in 
spelling  is  strictly  "  normal  "  and  that  the  real  variability  is 
alike  in  all  grades.  In  a  later  section  we  shall  take  up  the  matter 
of  applying  to  our  results  distributions  which  are  not  normal. 
Meanwhile,  however,  it  will  be  interesting  to  observe  how  satis- 
factory a  strictly  normal  form  of  distribution  proves  to  be.  To 
the  extent  that  it  expresses  the  same  or  nearly  the  same  facts 
as  the  record  (so  far  as  it  should,  if  valid,  do  so),  it  shows  its 
value. 

1.  In  Fig.  21  the  20  surface  of  frequency  does  not  reach  the 
4th-grade  median;  but  it  only  falls  short  a  little.  According  to 
the  record  in  the  Easy  50-Word  Test  no  2.a  child  did  as  well 
as  the  median  4th  grade  child.  But  the  best  2a  record  was  82% 
which  is  only  a  little  less  than  M^  (88.12  by  Table  XXI). 

2.  In  the  graphic  showing  the  3d-grade  distribution  does  not 
quite  reach  the  8th-grade  median.  Similarly  the  record  shows 
that  no  3d-grade  child  obtained  a  score  equal  to  94.68  which 
(Table  XI,  p.  27)  is  M^  for  the  Selected  100-Word  List;  al- 
though 3  third-grade  pupils  had  score.^  in  the  91  to  95  group. 
(Table  XI,  column  2.) 

3.  By  the  figure  we  see  that  the  low  end  of  the  8th-grade 
distribution  falls  short  of  M^  but  not  of  M^.     In  the  record  the 


62         spelling  Ability — Its  Measurement  and  Distribution 


O"       Ji  rt  <u  C 

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tH        t«       C 


5  •^.  J3      ^  ro 


2l.^ 


en   C   •  •. 

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^  o  o  c  !! 

L-    ?i  <+-■  J2  .11 


rt   —    O  -»—   u]    1 1  -^ 
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P  c  > 


c        y  C  ^     ^  M 
c  m  >  o       ^"  C 

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C.ti  t,^  II   II 

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o.  "2  <"  '-S  II  II 


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Observations  on  the  Distributions  Shown  in  Fig.  21  63 

same  is  true,  although  the  poorest  8th-graders  surpassed  the 
median  of  the  3d  grade  by  more  than  the  figure  would  indicate 
(See  Table  XI,  page  27). 

4.  The  2b  curve  at  its  low  end  does  not  reach  zero  (record). 
No  3d-grade  child  was  rated  o  in  the  Easy  50- Word  Test  (Table 
XXI,  p.  57). 

5.  The  most  remarkable  thing  in  the  figure  is  the  fact  that 
the  high  end  of  the  2a-grade  distribution  extends  above  the  low 
end  of  the  8th-grade  distribution.  Even  with  all  the  recent 
information  about  retardation,  acceleration,  mental  defect,  and 
precocity  combined  with  mis-grading  and  forced  promotions, 
some  critics  will  be  hardly  prepared  to  believe  that  any  children 
classified  in  the  first  half  of  the  second  year  of  school  life  can 
do  as  well  in  spelling  as  the  poorest  who  are  classified  in  the 
8th  (last  elementary)  year.  This,  however,  the  figure  shows; 
and  there  is  good  evidence  in  our  record  to  support  it.  We 
cannot  compare  these  extreme  grades  directly  because  they  did 
not  write  the  same  test.  But  in  Table  XI  (page  2y)  we  observe 
that  for  the  Selected  List  one  8th-grade  pupil  is  in  the  56-60 
group.  As  a  matter  of  fact  his  paper  was  rated  at  exactly  56%. 
Therefore  all  the  3d-grade  children  in  groups  above  51  to  55  did 
as  well  or  better.  This  proves  to  be  22.5%  of  the  3d-grade 
children.  It  is  remarkable  that  between  one-quarter  and  one- 
fifth  of  our  3d-grade  children  do  as  well  or  better  than  the 
poorest  8th-grade  child.  But  this  is  not  all.  In  the  Easy  50- 
Word  Test  the  highest  2a  score  was  82%.  Only  38  out  of  168 
3d-grade  children,  or  22.6%,  did  better.  See  Table  XXI,  page 
57.  (The  one  child  in  group  81-90  in  the  20  column  was 
rated  82.  In  the  3d-grade  column,  of  the  30  in  group  81-90  and 
the  21  in  group  91-100  combined,  38  were  rated  above  82%.) 
We  therefore  find  that  the  best  2a  child  and  the  poorest  8th- 
grade  child  are  equalled  or  surpassed  by  the  same  group  of 
3d-grade  children, — i.e.,  22y2%.  Hence  the  best  2a  child  and 
the  poorest  8th-grader  of  our  record  do  have  the  same  ability. 
To  show  this  fact,  the  2a  curve  should  pass  slightly  beyond  the 
low  end  of  the  8th-grade  curve,  as  in  fact  it  does.  This  may 
seem  to  be  drawing  over-fine  conclusions,  but  it  is  probable  that 
the  real  overlapping  is  as  great  as  the  record  shows.  If,  out 
of  so  few  2a  children  (175),  one  was  found  who  scored  82%, 


64         Spelling  Ability — Its  Measurement  and  Distribution 

it  is  likely  that,  with  a  much  larger  number,  there  would  not  only 
be  more  children  at  82%  but  some  at  even  higher  rating. 
Similarly  it  is  likely  that  if  a  much  greater  number  of  8th-year 
children  had  been  tested  some  would  have  obtained  less  than 
56%.  To  the  extent  that  either  one  or  both  of  these  proba- 
bilities were  true,  the  overlapping  would  somewhat  exceed  that 
which  the  record  suggests. 

6.  After  the  argument  of  the  last  paragraph  it  need  hardly 
be  said  that  there  is  both  in  the  graphic  representation  by  theory 
and  in  the  actual  record  an  overlapping  of  every  grade  distribu- 
tion on  every  other  from  low  2d  to  8th. 

The  location  of  the  zero-point  enables  us  to  draw  some  inter- 
esting conclusions  which  were  not  possible  before.  A  few  of 
these  will  be  briefly  stated.  Taking  the  medians  of  each  grade 
as  indicating  typical  abilities,  regarding  the  estimated  zero-point 
as  the  true  one,  assuming  normal  distributions  and  equal  real 
variabilities  for  all  grades,  and  defining  "  to  spell  twice  as  well  " 
as  "to  spell  words  of  twice  as  much  dvfUculty,"  Fig.  21  shows 
that  2&  children  are  more  than  twice  as  good  spellers  as  2a 
children,  and  that  3d-graders  are  about  three  times  as  capable, 
and  4th-graders  4  times  as  capable.  Fifth-grade  children  spell 
twice  as  well  as  2h  children.  Eighth-grade  children  are  only 
twice  as  good  as  3d-grade  children.  This  last  statement  means 
that  typical  children  who  have  reached  the  3d  grade  have  half 
as  much  spelling  ability  as  is  required  of  the  average  child  in  the 
last  year  of  the  elementary  school. 

We  have  in  Fig.  21  a  representation  by  which  the  entire  range 
of  difficulty  of  spelling  words,  appropriate  to  the  elementary 
school,  may  be  shown.  The  notation  below  the  base-line  shows 
the  positions  within  that  range  taken  by  the  10  words  of  our 
scale  which  stand  at  equal  intervals  upon  it  (Table  XX, 
page  52).  Since  these  words  include  both  the  easiest  word 
("  only  ")  and  the  hardest  ("  too  ")  of  the  entire  scale  they  show 
its  total  spread.  It  will  therefore  be  seen  to  what  extent  the 
statement  is  true  which  was  made  at  the  beginning  of  Section 
14  to  the  effect  that  with  these  50  words  we  have  only  suc- 
ceeded in  scaling  "  a  limited  segment  of  the  entire  projection 
representing  spelling  ability."  By  actual  measurement  it  appears 
that  this  segment  is  but  a  trifle  more  than  one-fifth  of  the  entire 


Supplementary  Testing  at  Schools  VI  and  VII  65 

projection.  It  will  now,  however,  become  apparent  that  no 
greater  segment  could  have  been  so  scaled  reliably  from  the 
limited  material  at  our  disposal.  By  reference  to  Fig.  21  it  will 
be  seen  that  no  words  easier  than  "  only  "  could  have  been  used 
and  still  have  been  clearly  within  the  8th-grade  distribution.  On 
the  other  hand  no  word  that  scales  much  higher  than  "  too  " 
could  have  been  used  and  still  have  been  clearly  within  the  3d- 
grade  distribution.  With,  say,  ten  thousand  children  of  each 
grade  tested  each  wdth  a  longer  list,  a  wider  spread  could  have 
been  obtained.  The  series  of  fifty  words  which  we  used  spreads 
over  nearly  the  whole  of  the  base-line  common  to  both  the  3d- 
and  8th-grade  curves. 

It  is  evident,  therefore,  that  much  remains  to  be  done  to  perfect 
a  scale  which  shall  pretend  to  completeness.  Some  of  this  fur- 
ther scaling  will  be  undertaken  in  a  later  section  of  this  mono- 
graph. A  great  deal  must  be  left  for  later  studies.  A  great 
many  more  w'ords  must  be  used  both  to  fill  in  the  gaps  within 
the  present  scale  and  to  extend  its  limits.  Our  main  purpose  has 
been  to  show  the  theory  and  technique  required. 

§  16.  Supplementary  Testing  at  Schools  VI  and  VII 
After  the  data  thus  far  given  were  in  hand  the  same  test 
material  was  used  in  two  other  schools.  The  results  of  this 
supplementary  testing  are  now^  given.  The  Selected  List  (100 
words)  was  dictated  during  the  fall  term  of  1912  at  schools 
VI  and  VII  to  1770  children.  Two  of  the  assistants  in  psy- 
chology at  Teachers  College  acted  as  examiners,  and  the  papers 
were  then  scored  for  individual  ratings,  but  not  for  word  ratings. 
Table  XXV  gives  the  distribution  of  these  ratings  and  the  grade 
medians  for  these  two  schools.  Table  XXVI  gives  the  com- 
parisons by  grades  of  the  combined  results  in  schools  VI  and  VII 
with  those  in  schools  II,  III,  IV,  and  V  taken  together.  The 
comparison  shows  that  in  general  schools  VI  and  VII  did  not  do 
so  well  as  those  tested  earlier.  On  the  average  the  grade  medians 
are  nearly  6^  per  cent  lower. 

To  one  who  would  expect  close  conformity  to  our  previous 
individual  ratings  in  the  case  of  any  school  taken  at  random, 
this  discrepancy  will  be  disappointing.  But  to  one  who  recog- 
nizes the  wide  variability  among  schools  in  every  subject,  the 


66        Spelling  Ability — Its  Measurement  and  Distribution 


TABLE  XXV 

Distribution  of  Individual  Ratings,  Schools  VI  ajstd  VII. 
Selected  (100)  List 


Per  Cent 

3d  Grade 

4th  Grade 

5th  Grade 

6th  Grade 

7th  Grade 

8th  Grade 

Correct 

No. 

% 

Mo. 

% 

No. 

% 

No. 

% 

No. 

% 

No. 

% 

0-  10 

69 

22.7 

10 

3.4 

1 

.3 

3 

1.2 

0 

0 

0 

0 

11-  20 

58 

19.1 

32 

10.8 

5 

1.7 

5 

2.0 

2 

.6 

0 

0 

21-  30 

65 

21.4 

29 

9.8 

12 

4.1 

8 

3.2 

2 

.6 

0 

0 

31-  40 

49 

16.1 

34 

11.5 

24 

8.3 

7 

2.8 

5 

1.5 

2 

.7 

41-  50 

29 

9.5 

40 

13.5 

31 

10.6 

13 

5.2        3 

.9 

1 

.3 

51-  60 

17 

5.6 

51 

17.6 

41 

14.1 

23 

9.2 

13 

3.9 

3 

1.0 

61-  70 

10 

3.3 

39 

13.2 

47 

16.2 

28 

11.2 

41 

12.2 

15 

5.1 

71-  80 

6 

2.0 

29 

9.8 

53 

18.3 

51 

20.4 

56 

16.6 

16 

5.5 

81-  90 

1 

.3 

25 

8.4 

58 

20.0 

51 

20.4 

114 

33.8 

97 

33.1 

91-100 

0 

0 

7 

2.4 

18 

6.2 

61 

24.4 

101 

30.0 

159 

54.3 

Totals... 

304 

296 

290 

250 

337 

293 

'V     • 

Medians. 

25.27 

51.75 

67.67 

79.36 

84.86 

91.96 

etc. 


TABLE  XXVI 

Comparison  of  Results  Obtained  in  Schools  VI  and  VII  with 
Those  Obtained  in  Schools  II,  III,  IV  and  V 
Figures  show  per  cent  of  pupils  in  each  grade  who  were  rated  0-10,  11-20, 


3d  Grade 

4th  Grade 

5th  Grade 

6th  Grade 

7th  Grade 

8th  Grade 

Per  Cent 

Sch. 

Sch. 

Sch. 

Sch. 

Sch. 

Sch. 

Sch. 

Sch. 

Sch. 

Sch. 

Sch. 

Soh. 

Correct 

II, 

II, 

II, 

II, 

II. 

II, 

III, 

VT, 

III, 

VI, 

III, 

VI. 

III, 

VI, 

III. 

VI, 

III, 

VI, 

IV,  V 

VII 

IV,  V 

VII 

IV,  V 

VII 

IV,  V 

VII 

IV,  V 

Vli 

IV,  V 

VII 

0-  10 

.     6.9 

22.7 

.4 

3.4 

.6 

.3 

0 

1.2 

0 

0 

0 

0 

11-  20 

.  15.2 

19.1 

4.7 

10.8 

.6 

1.7 

0 

2.0 

0 

.6 

0 

0 

21-30  

.  20.5 

21.4 

7.7 

9.8 

3.5 

4.1 

.5 

3.2 

0 

.6 

0 

0 

31-40  

.   16.1 

16.1 

12.0 

11.5 

4.6 

8.3 

.5 

2.8 

.5 

1.5 

0 

.7 

41-  50  

.   13.0 

9.5 

13.5 

13.5 

8.9 

10.6 

2.4 

5.2 

.8 

.9 

0 

.3 

51-  60  

.   11.2 

5.6 

12.4 

17.6 

10.1 

14.1 

5.0 

9.2 

2.2 

3.9 

.4 

1.0 

61-  70  

.     9.6 

3.3 

14.6 

13.2 

17.8 

16.2 

8.4 

11.2 

3.8 

12  2 

1.5 

5.1 

71-80  

.     4.7 

2.0 

17.1 

9.8 

21.0 

18.3 

19.6 

20.4 

13.4 

16.6 

6.9 

5.5 

81-90  

.     1.8 

.3 

12.7 

8.4 

19.6 

20.0 

.30.6 

20.4 

32.0 

33.8 

21.7 

33.1 

91-100 

.       .7 

0 

5.0 

2.4 

13.2 

6.2 

33.1 

24.4 

47.1 

30.0 

69.7 

54.3 

Medians .  . 

.  35.80 

25.27 

60.70 

51.75 

73.10 

67.67 

84.90 

79.36 

90.50 

84.86 

94.68 

91.96 

difference  will  occasion  no  surprise.  We  should  do  well  also  to 
bear  in  mind  not  only  that  schools  do  vary  greatly,  but  that  in 
this  particular  instance  there  was  a  constant  factor  tending  to 
lower  the  ratings.  In  the  supplementary  test  the  dictation  was 
given  by  a  stranger ;  in  the  original  test  by  the  class  teacher, 
guided  by  printed  directions.    Leaving  out  of  account  any  sugges- 


Supplementary  Testing  at  Schools  VI  and  VII  67 

tion  of  unfair  methods  on  the  part  of  teachers  for  the  purpose  of 
making  a  showing,  this  fact  is  quite  sufficient  to  account  for  a 
falling  off  of  results  in  schools  VI  and  VII  without  supposing 
them  to  be  much,  if  any,  inferior  to  the  others  in  the  ability  of 
their  children  to  spell.  The  teacher  has  but  one  class  to  examine 
and  she  takes  her  time.  She  doubtless  takes  full  advantage  of 
the  direction  permitting  the  reading  of  a  sentence  "  in  whole 
or  in  part  as  many  times  as  may  be  necessary  to  secure  its  full 
comprehension."  She  knows  her  class.  The  peculiarities  or 
defects  of  pupils  are  her  daily  concern  and  she  modifies  her 
appeal  accordingly.  The  children  are  at  ease  in  her  presence. 
They  know  her  voice  and  manner  of  speaking;  and  they  more 
readily  understand  her  than  they  would  another.  In  these 
matters  they  are  placed  at  a  disadvantage  when  examined  by  a 
stranger. 

We  should  expect  this  disadvantage  to  be  most  evident  in 
the  lower  classes;  and  an  inspection  of  the  medians  of  Table 
XXVI  shows  how  strikingly  this  is  true.  The  children  of  the 
3d  grade  fell  off  10.5%  ;  of  the  4th,  9%  ;  of  the  5th,  6th,  and  7th 
approximately  5.5%;  and  of  the  8th  only  2.5%.  The  force, 
whatever  its  nature,  tending  to  depress  the  results  at  schools  VI 
and  VII  was  clearly  operative  to  a  greater  degree  in  the  lower 
classes  and  to  a  much  less  degree  in  higher  classes.  The  effect  of 
a  change  from  the  class  teacher  to  a  stranger  as  examiner  would 
be  expected  to  bring  about  results  of  just  such  a  nature. 

But  the  obvious  advantage  of  having  the  same  examiner  for 
every  class  (in  this  case  there  were  two  working  together)  is  that 
however  the  results  in  general  may  be  lowered,  there  is  a  better 
opportunity  to  compare  class  with  class  or  grade  with  grade, 
or  school  with  school. 

The  real  reason  why  this  supplementary  testing  was  under- 
taken was  to  verify  the  median  intervals  that  had  been  derived 
from  the  original  testing.  The  fact  of  classes  being  examined 
by  the  same  persons  is  of  great  value  for  this  purpose.  If,  with 
this  factor  of  the  examiner  made  constant,  we  find  that  these 
median  distances  in  spite  of  a  falling  off  of  grade  performances 
remain  substantially  the  same,  we  shall  be  justified  in  feeling  that 
our  former  results  are  reasonably  reliable. 


68         Spelling  Ability — Its  Measurement  and  Distribution 

TABLE  XXVII 

Number  and  Per  Cent  of  Pupils  in  Each  Grade  Whose  Ability  Equalled 

OR  Exceeded  that  of  the  Median  Pupil  in  Every  Other  Grade, 

WITH  the  P.E.  Values  Corresponding  to  Each  Per  Cent. 

Schools  VI  and  VII  Combined  with  Schools  II,  III, 

IV  AND  V 


3d 
Grade 

4th 
Grade 

5th 
Grade 

6th 
Grade 

7th 
Grade 

8th 
Grade 

3d  grade. .  . 
N=749. .  .  . 

No. 

% 
P.E. 

110 
14.7 
1.55 

38 
5.1 
2.425 

12 
1.6 
3.18 

4 

.5 
3.82 

0 
0 

? 

4th  grade.  . 
N=763. . . . 

No. 

% 
P.E. 

619 

81.1 
—1.31 

223 

29.2 

.81 

90 
11.8 
1.76 

45 
5.9 
2.32 

16 
2.1 
3.01 

5th  grade .  . 
N=805. .  .  . 

No. 

% 
P.E. 

758 

94.2 
—2.33 

584 
72.5 
—  .89 

227 
28.2 
.86 

121 
15.0 
1.54 

47 
5.8 
2.33 

6th  grade . . 
N=668. . .  . 

No. 

% 
P.E. 

655 

98.1 
—3.08 

597 

89.4 
—1.85 

511 

76  5 
—1.07 

241 
36.1 
.55 

112 
16.8 
1.43 

7th  grade . . 
N=702. .  .  . 

No. 

% 
P.E. 

698 

99.43 
—3.75 

678 

96.6 
—2.71 

615 

87.6 
—1.71 

482 
68.7 
—  .72 

188 
26.8 
.92 

8th  grade .  . 
N=570. .  .  . 

No. 

% 
P.E. 

570 
100.0 
? 

565 
99.12 
—3.52 

544 

95.44 
—2.50 

502 

88.1 
—1.75 

428 

75.1 
—1.00 

In  Table  XXVII  we  give  the  number  and  per  cent  of  pupils 
who  equal  or  surpass  the  medians  of  other  grades  than  their 
own  with  the  corresponding  P.E.  values.  In  this  table  are  com- 
bined the  children  who  were  examined  at  schools  VI  and  VII 
with  those  examined  at  schools  II,  III,  IV  and  V,  It  is  to  be 
compared  with  Table  XV  (page  36).  Table  XXVIII  gives  the 
median  distances  as  derived  from  the  P.E.  values  of  Table 
XXVII.  Compare  with  Table  XVI  (page  39).  The  average 
distances,  1.37,  .87,  .90,  .66,  and  .86,  are  to  be  compared  with 
the  values  for  the  same  distances  as  derived  on  page  39,  namely 
(correct  to  2  decimal  places)  1.35,  .84,  1.05,  .66,  and  .91.  Only 
in  the  case  of  M.,_p,  is  there  an  important  difference.  The  average 
difference,  including  that  of  Mr,.^,,  is  .05  ;  excluding  it,  the  average 
difference  is  but  .025.    The  entire  range  from  M^  to  Mj,  is  found 


Arrangement  of  Words  of  List  by  Teachers'  Judgments       69 

to  be  4.66  as  compared  with  4.81  according  to  the  primary 
testing.  These  correspondences  are,  we  feel,  quite  close  enough 
to  establish  the  essential  reliability  of  our  original  figures. 


TABLE  XXVIII 

Median  Distances  Derived  from  the  P.E.  Values  of  Table  XXVII 


Average 


M, 


1.55 
(direct) 

1.61 

(^3-5-^^.1-5) 

1.42 
(iWg-e— Afi-e) 

1.50 
? 

1.31 

(direct) 

1.44 
1.23 

1.04 

(M,_3-M,_,) 

? 


1.37 


M, 


.87 

(M3_5-ilf3_,) 

.81 
(direct) 

.90 
(M,_6-M5_e) 

.78 

.68 

(M,_8-i»/5_8) 

1.02 
(M5_3-M,_3) 

.89 
(direct) 

.78 
1.00 
1.02 


.87 


M. 


.76 

{M,_,-M,_:) 

95 

(3f,_,-M,_,) 

.86 
(direct) 

99 
(ilV-Mg_,) 

.90 

.75 

.96 

1.07 
(direct) 

99 

(M,_5-i/7_e) 

.75 


.90 


M„ 


.!/._ 


.64 

.56 

(M,_-.l/,_„) 

.68 
(M5_,-M5_,) 

.55 

(direct) 

.51 

(Me_3-3/,_,) 

.67 

(M7_3— il/6_3) 

.86 
(M,_,-.l/,_,) 

.64 

(M,_,-3/,_,) 

.72 
(direct ) 

.75 

(Mg_e— il/8_7) 


.66 


(M3_8— M3_7) 

.69 
(M,_3-A/,_,) 

.79 


.92 
(direct ) 


.81 
(3/3_,-.¥,_p 

.79 
(JV,-.l/,_,) 

1.03 

1.00 
(direct) 


.86 


§    17.     Arrangement  of  the   Words  of  the  Preferred  List  by 
Teachers'   Judgments 

A  certain  order  of  difficulty  of  the  50  words  of  the  Preferred 
List  having  been  determined  as  the  result  of  testing  in  five 
schools  and  to  a  certain  extent  verified  by  a  record  from  two 
other  schools  (Table  XIX,  and  Fig.  20).  a  comparison  of  the 
result  with  an  arrangement  of  the  same  words  based  on  the 
judgment  of  teachers  becomes  interesting.     It  has  an  important 


70         Spelling  Ability — Its  Measurement  and  Distribution 

bearing  on  the  whole  spelHng  situation  because  it  is  by  individual 
judgment  as  to  the  difficulty  of  words  that  lists  are  made  up 
and  graded  for  classes,  schools,  or  systems  of  schools.  How 
far  such  grading  is  reliable  may  be  gathered  by  finding  out  to 
what  extent  individual  judgment  squares  with  the  results  of 
actual  testing. 

For  this  purpose  the  50  w^ords  of  the  Preferred  List  were 
arranged  alphabetically  and  distributed  to  a  number  of  teachers. 
They  w^ere  asked  to  arrange  the  words  in  what  they  judged  to  be 
their  order  of  difficulty  for  children  to  spell,  beginning  with 
the  easiest.  They  were  particularly  requested  to  do  the  work 
without  consulting  any  one.  Two  hundred  arrangements  were 
secured.  They  differed  widely — so  widely  that  whatever  may 
be  the  value  of  a  consensus  of  many  individuals,  the  trust- 
worthiness of  the  judgment  of  a  single  teacher  appears  to  be 
almost  of  no  value.  It  may  be  good  and  it  may  be  bad ;  and  it 
is  about  as  likely  to  be  the  one  as  the  other.  With  one  notable 
exception,  the  agreement  with  the  record  was  closer  for  the 
easiest  and  hardest  words  than  for  those  of  medium  difficulty. 
This  might  have  been  expected  from  the  fact  that,  as  shown  in 
Fig.  20,  the  words  at  the  ends  of  the  scale  differ  by  larger 
amounts  than  do  those  nearer  the  middle.  The  exception 
referred  to  is  the  word  "  too,"  which,  although  it  was  in  every 
school  the  hardest  word  to  spell,  was  by  more  than  a  fourth 
of  the  teachers  judged  to  be  actually  the  easiest,  or  next  to  the 
easiest,  in  the  list.  The  deviation  of  individual  judgments  from 
the  record  is  shown  by  figures  taken  from  a  random  sampling  of 
the  two  hundred  teachers'  arrangements.  Five  such  arrange- 
ments being  taken  by  chance  from  the  whole  number,  proved  to 
be  those  of  teachers  No.  7,  No.  88,  No.  109,  No.  134,  and  No. 
178.  They  ranked  the  5th,  loth,  15th,  20th,  ....  50th  words 
(record)  as  follows: 

Record  5,  10,  15,  20,  25,  30,  35,  40,  45,  50 

No.      7  22,15,    1,31,34,33,38,47,14,10  r=+0.09 

No.    88  15,    9,    4,41,13,24,33,35,20,    1  r=  +  0.15 

No.  109  9,  11,  18,  39,  35,  36,  22,  25,  29,  10  r=+0. 15 

No.  134  24,  22,  2.3,  20,    6,  44,    7,  42,  35,  11  r=— 0.03 

No.  178  21,    2,    7,22,14,29,49,38,28,    1  r=+0.2 


Arrangement  of  Words  of  List  by  Teachers'  Judgments       71 

J 
It  is,  however,  to  be  expected  that  when  a  large  number  of 
judgments  are  taken  together,  wide  disagreements  with  a  true 
arrangement  will  tend  to  disappear,  and  a  resultant  will  be 
obtained  that  may  be  expected  to  be  closer  to  the  facts  than 
any  single  judgment  would  ever  be  likely  to  be.  The  statistical 
treatment  of  the  200  judgments  was  based  on  the  theorem, 
"  Difterences  that  are  equally  often  noticed  are  equal,  unless  the 
differences  are  either  always  or  never  noticed."  It  is  an  abbre- 
viation of  the  method  used  by  Professor  Thorndike  in  deriving  his 
scale  for  Handwriting  and  by  Dr.  Hillegas  in  his  similar  work  for 
English  Composition.  We  have  not  felt  the  necessity  of  making 
comparisons  of  the  judgment  of  each  word  with  that  of  every 
other  word,  because  the  nature  of  our  material  has  enabled  us 
to  derive  our  scale  by  a  more  direct  method.  Since  we  are  here 
concerned  with  a  comparison  only,  we  have  been  content  to 
proceed  as  follow' s :  The  record  shows  "  only  "  to  be  easier 
than  "  even."  What  per  cent  of  the  individuals  who  arranged 
the  words  for  difficulty  so  judged?  As  betw'een  "even"  and 
"  smoke  "  :  "  smoke  "  and  "  chicken  "  ;  "  chicken  "  and  "  front  " ; 
etc.,  what  per  cent  of  the  judgments  indicate  that  the  first  word 
of  each  pair  is  easier  than  the  second,  as  the  record  shows?  The 
following  is  found  to  be  true  for  the  first  six  words: 

"only"         was  judged  easier  than  "even"  by  38.5%  of  the  judges. 

"  even "           "          "            "          "      "  smoke "  "    67.5%    "  "         " 

"  smoke "        "          "            "          "      "  chicken "  "    72.0%    "  "         '' 

"chicken"      "          "            "          "      "front"  "    48.070    "  " 

"front"          "          "           "          "      "another"  "   53.0%    "  " 

Now  when  the  difficulty  of  a  word  is  judged  by  a  very  great 
number  of  judges  some  will  overestimate  its  difficulty,  others  will 
underestimate  it.  Those  who  make  small  errors  will  be  more 
numerous  than  those  who  make  large  errors.  The  frequency 
of  the  judgments  wall  take  the  form  of  the  curve  of  the  proba- 
bility integral  whose  base-line  represents  the  amounts  of  difficulty 
which  the  word  in  question  is  judged  to  have.  The  point  on  the 
base-line  which  corresponds  to  the  greatest  frequency  of  judg- 
ments represents  the  central  tendency  of  the  judges  in  rating 
the  word.  It  is  therefore  the  point  which  represents  the  difficulty 
of  the  word  as  determined  by  individual  judgments.  Two  or 
more  words  may  be  compared  for  difficulty  if  we  know  the  per 


72         spelling  Ability — Its  Measurement  and  Distribution 


cent  of  judges  who  rate  one  word  easier  (or  harder)  than  the 
other. 

Fig.  22  shows  the  curves  for  the  first  six  words  arranged  to 
show  the  per  cent  of  "  easier "  judgments  noted  above.  The 
curve  for  "  even  "  is  so  placed  that  38.5%  of  its  area  is  to  the 
right  of  YO — the  median  axis  of  the  curve  for  "  only  "  when  that 

TABLE  XXIX 

Comparison  of  Results  by  Teachers'  Judgments  and  by  the 
Record.    Preferred  List 


Word- 

Num- 

ber 

(scale) 

Word 

%of 

times 

each 

word  was 

judged 

easier 

than  the 

following 

word 

Rank 

Word- 
Num- 
ber 
(scale) 

%  of 

times 

each 

word  was 

judged 

easier 

than  the 

following 

word 

Rank 

By 
Teach- 
ers' 
Judg- 
ments 

By 
the 
Re- 
cord 

Word 

By 

Teach- 
ers' 
Judg- 
ments 

By 
the 
Re- 
cord 

3 
1 

only 

even 

smoke 

chicken .... 
front 

another . . . 

lesson 

bought.  .  .  . 

pretty 

nails 

butcher .  .  . 
Tuesday. . . 

sure 

answer.  .  .  . 
nor 

raise 

cousin  .... 
beautiful .  . 

touch  

freeze 

forty 

instead. .  .  . 

wear 

tailor 

tying 

38.5 
67.5 
72.0 
48.0 
53.0 

39.5 

86.0 
29.5 
27.5 
89.0 

65.5 
19.5 
74.5 
10.0 
90.0 

69.0 
53.0 
41.5 
29.6 
31.5 

75.0 
33.0 
44.0 
72.5 
55.0 

2 
1 
3 
7 
6 

8 

4 
18 
10 
11 

19 
29 
13 

21.5 
5 

21.5 

37 

39 

33 

20 

12 
24 
17 
14 
25.5 

1 
2 
3 
4 
5 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15.5 

15.5 

17.5 

17.5 

19 

20 

21.5 

21.5 

23 

24.5 

24.5 

14 

7 
40 
38 
43 

13 

17 
33 
44 
30 

20 
23 
19 

24 
47 

37 
29 
36 
18 
34 

26 
32 
27 
31 
39 

minute. 

25.5 
51.0 
69.0 
56.0 
15.5 

79.5 

81.0 
39.5 
43.5 
77.0 

44.5 
21.5 
87.0 
29.0 
54.0 

27.0 
56.0 
54.5 
58.0 
35.5 

91.5 
16.0 
64.0 
21.0 

27 

15 
16 
25.5 

28 

9 
23 
44 
40 
35 

48 
46 
30 
49 
43 

45 
31 
36 
38 
41 

34 

50 
42 
47 
32 

26 
27 

4 

towel .  . 

28 

28 
5 

tobacco 

29 
30 

9 

2 

8 

11 

16 

button  . 
janitor  . 
quarrel . 
against. 

31 
32 
33 
34 
35 

46 

36. 

41 

6 

45 

25 

whistle. 

stopping 

carriage 

36.5 
38 
39 
40 

49 
15 
50 
22 

telephone. . 
choose  .... 
telegram. .. 

41 
42 
43 
44 

21 

45 

10 

48 

already 

46 
47 

12 
35 

beginning. . 

48 
49 

42 

50 

axis  is  produced;  67.5%  of  the  curve  for  "smoke"  is  to  the 
right  of  Y^O'^  produced;  72%  of  the  curve  for  "  chicken  "  is  to 
the  right  of  Y'^O^  produced ;  and  so  on.  H  0^  is  the  difference 
in  difficulty  between  "  only "  and  "  even  " ;  K  O^,  between 
"  even  "  and  "  smoke  "  ;  P  0\  between  "  smoke  "  and  "  chicken  "  ; 
5"  O*,  between  "  chicken  "  and  "  front  " ;  and  T  0^,  between 
"  front "  and  "  another."  When  less  than  50%  of  the  judges 
regard  the  first  of  a  pair  of  words  as  easier,  the  second  is,  of 


Arrangement  of  Words  of  List  by  Teachers'  Judgments       73 

Y 


Fig.  22.     Diagram    showing    difference    in    difficulty  between  words    by 

Teachers'  Judgments. 


74        Spelling  Ability — Its  Measurement  and  Distribution 

course,  judged  the  easier,  and  the  difference  in  difficulty  is  a  nega- 
tive one.  Such  is  the  case  in  the  only-even  and  chicken-front 
pairs.  The  scaling  of  these  six  words  is  diagrammatically  shown 
in  Fig.  22  by  producing  each  median  vertical  to  meet  the  line  AB. 
It  will  be  seen  that  the  order  of  difficulty  is  not  the  same  as 
the  order  obtained  by  testing. 

Table  XXIX  shows  for  the  entire  50  words  the  per  cent  of 
teachers  who  judged  each  word  easier  than  the  following  word 
and  the  rank  of  each  word  for  difficulty  by  record  and  by 
teachers'  judgments.  In  spite  of  the  fact  that  the  opinion  of 
single  teachers  is  so  unreliable,  the  combined  judgments  of  a 
group  as  large  as  200  yield  an  arrangement  which  agrees  closely 
enough  with  the  arrangement  by  record  to  confirm  and  support 
the  latter  in  no  small  degree.  The  correlation,  by  the  '  foot-rule ' 
method,  is  found  to  be  0.79,  which  may  quite  properly  be 
regarded  as  satisfactory. 

It  may  be  worth  while  to  point  out,  however,  that  in  practice 
the  selection  and  arrangement  of  words  for  teaching  are  not  the 
work  of  a  large  number  of  individuals.  These  things  are  usually 
done  by  a  single  teacher  for  a  class  or  by  a  text-book  writer  for 
as  many  classes  as  use  his  book.  Not  two  hundred,  probably  not 
even  ten,  persons  judge  as  to  the  selection  and  arrangement  of 
the  words  in  the  lists  now  used  in  most  schools.  The  length  of 
such  lists,  moreover,  would  seem  to  preclude  the  possibility  of 
a  satisfactory  judgment  as  to  difficulty  by  individuals.  Probably 
if  our  own  list  of  50  words  had  been  shorter,  the  teachers  would 
have  worked  more  accurately.  The  several  thousand  words  in 
a  spelling-book  certainly  constitute  a  list  about  which  there  may 
be  expected  to  be  wide  and  numerous  disagreements.  We  alluded 
in  Section  3  above  to  our  attempt  to  secure  for  school  use  a 
500Q-word  vocabulary  graded  by  years  and  based  upon  the  agree- 
ments of  five  spelling-books.  This  task  proved  to  be  very  difficult 
precisely  because  of  the  total  absence  of  agreement  as  to  grading 
in  the  case  of  hundreds  of  words.  One  speller  would  assign 
words  to  the  third  grade  which  another  would  put  in  the  sixth, 
seventh,  or  eighth.  Gradings  three,  four,  and  even  five  years 
apart  occurred  with  remarkable  frequency. 

The  obvious  way  (and  the  necessary'  way,  it  would  seem)  to 
grade  words  for  difficulty  is  not  by  some  one's  opinion  of  how 


i 


Rice  Sentence  Test.     Easy  50-Word  Test  75 

hard  they  are,  but  by  actually  "  trying  them  out."  In  matters  of 
handwriting  and  composition  the  judgment  of  individuals  is  all- 
important,  because  merit  in  either  is  precisely  a  matter  of  judg- 
ment. One  sample  is  better  than  another  only  because  competent 
persons  think  so.  On  the  contrary,  one  word  is  harder  to  spell 
than  another  not  because  we  think  so,  but  because  more  people 
misspell  the  one  than  the  other,  or  because  it  takes  more  time  to 
learn  to  spell  the  one  than  the  other.  It  is  strange,  therefore, 
that  no  spelling-book  has  yet  appeared  based  upon  a  study  of 
how  frequently  children  misspell  the  words  of  which  it  is  com- 
posed. In  fact  no  study  of  spelling,  that  we  know  of,  has  done 
more  than  obtain  individual  ratings  of  pupils,  based  on  the  tacit 
assumption  that  the  words  used  are  all  equally  difficult  to  spell. 
No  investigation  has  been  thought  necessary  of  the  words  them- 
selves. The  results  of  this  section,  although  by  no  means 
thoroughly  worked  out,  sufficiently  indicate  the  present  unrelia- 
bility of  individual  judgment  with  regard  to  w^ords,  unless  the  list 
is  very  short  and  the  judgments  very  numerous.  It  is  quite 
possible  that  at  some  later  time,  after  studies  of  words  based  on 
actual  tests  have  been  frequently  made,  our  judgment  of  word 
difficulties  may  be  greatly  improved.  Our  opinion  as  to  how  hard 
words  are  might  then  become  a  valuable  supplement  to  the 
conclusions  of  the  investigator. 

§  18.     Rice  Sentence  Test.    Easy  ^o-Word  Test 

During  the  middle  week  of  the  fall  term  of  1912,  the  sentence 
test  used  by  Rice — and  afterwards  by  Cornman — was  dictated 
to  1984  pupils  in  schools  II,  III,  and  VIII.  Children  of  the  4th 
and  5th  grades  wrote  sentences  containing  50  words ;  those  of  the 
6th.  /th,  and  8th  grades  wrote  41  of  the  same  words  together  with 
36  additional  words — yy  in  all.    The  entire  test  follows  : 

Rice  Sentence  Test 

\\^hile  running  he  slipped.  I  listened  to  his  queer  speech,  but 
I  did  not  believe  any  of  it.  The  weather  is  changeable.  His  loud 
whistling  frightened  me.     He  is  always  changing  his  mind.    His 


76         Spelling  Ability — Its  Measurement  and  Distribution 


chain  was  loose.  She  was  baking  cake.  I  have  a  piece  of  it.  Did 
you  receive  my  letter?  I  heard  the  laughter  in  the  distance. 
Why  did  you  choose  that  strange  picture?  ^Because  I  thought 
I  Hked  it.  It  is  my  purpose  to  learn.  Did  you  /o.y^  your  almanac  f 
I  gave  it  to  my  neighbor.  *I  was  writing  in  my  language  book. 
Some  children  are  not  careful  enough.  Was  it  wtYrj^ary  to  keep 
me  waiting  so  long?  Do  not  disappoint  me  so  often.  I  have 
covered  the  mixture.  He  is  getting  better.  *A  feather  is  /I'^y./jf. 
Do  not  deceive  me.  I  am  driving  a  new  horse.  *Is  the  surface 
of  your  desk  rough  or  smooth?  The  children  were  hopping. 
This  is  certainly  true.  I  was  very  grateful  for  my  elegant  present. 
If  we  have  patience  we  will  succeed.  He  met  with  a  .yfTZ'^r^:- 
accident.  Sometimes  children  are  not  sensible.  You  had  no 
business  to  answer  him.  You  are  not  sweeping  properly.  Your 
reading  shows  improvement.  The  ride  was  very  fatiguing.  I  am 
very  anxious  to  hear  the  news.  I  appreciate  your  kindness  I 
assure  you.  I  cannot  imagine  a  more  peculiar  character.  I 
guarantee  the  book  will  meet  with  your  approval.  Intelligent 
persons  learn  by  experience.  The  peach  is  delicious.  I  realize 
the  importance  of  the  occasion.  Every  rule  has  exceptions.  He  is 
thoroughly  conscientious;  therefore  I  do  trust  him.  The  elevator 
is  ascending.    Too  much  praise  is  not  wholesome. 


TABLE  XXX 
Distribution  of  Individual  Ratings.     Rice  Sentence  Test. 


Per  Cent  Correct 

4th  Grade 

5th  Grade 

6th  Grade 

7th  Grade 

8tli  Grade 

No. 

% 

No. 

% 

No. 

% 

No. 

% 

No. 

% 

0-   10 

38 
54 
61 
55 

72 
74 
59 
54 
31 
9 

7.5 
10.7 
12.0 
10.8 
14.2 
14.6 
11.6 
10.7 
6.1 
1.8 

3 
13 

18 
49 
62 
76 
76 
91 
65 
17 

.6 

2.8 
3.8 
10.4 
13.2 
16.2 
16.2 
19.4 
13.8 
3.6 

2 
13 
21 
46 
53 
80 
70 
62 
40 

9 

.5 

3.3 

5.3 

11.6 

13.4 

20.2 

17.7 

15.7 

10.1 

2.3 

0 
3 
5 

20 
32 
52 
53 
77 
95 
30 

0 

.8 

1.4 

5.4 

8.7 

14.2 

14.4 

21.0 

25.9 

8.2 

0 

0 

0 

0 

2 

15 

37 

61 

96 

33 

0 

11-20 

21-  30 

0 
0 

31-  40 

0 

41-  50 

.8 

51-60 

6.1 

61-  70 

15.2 

71-80 

81-  90 

25.0 
39.3 

91-100 

13.5 

Totals 

Medians 

507 

48.17 

470 

64.13 

396 

58.57 

367 

73.86 

244 

82.07 

Rice  Sentence  Test.     Easy  jo-Word  Test 


77 


The  4th-  and  5th-year  test  ends  with  "  This  is  certainly  true." 
The  test  for  the  upper  grades  comprises  all  the  sentences  except 
the  four  marked  with  an  asterisk.    The  test  words  are  italicized. 

The  principal  object  in  giving  this  test  was  to  obtain  scores 
for  a  new  series  of  words  by  which  the  grade  and  general  scales 
(Figs.  14-20)  could  be  supplemented  and  extended.  The  papers, 
however,  were  also  rated  for  individual  performances.     Subject 


/O 


J L 


/O     2.0    30     ¥0    ^0    60    70     SO   ^0    100 


20 

/s 


0       10     ZO    30     ^C    SO     60     70     §0    70     /oo 

Fig.  23.     Relative  frequencies  of  different  percentages  correct,  4th  grade; 

Rice  Sentence  Test ;  Table  XXX. 
Fig.  24.     Same  as  Fig.  23,  but  for  5th  grade. 

to  the  limitations  of  regarding  all  words  as  equal,  the  results  on 
this  basis  may  be  used  to  supplement  those  of  Rice  and  Cornman. 
Rice  gives  nothing  but  grade  averages,  and  Cornman  gives  the 
same  for  two  tests  after  an  interval  of  one  year.  We  shall 
continue  to  use  the  median  as  a  measure  of  central  tendency  and 
shall  give  a  distribution  of  pupils'  ratings  for  each  grade.  Table 
XXX  gives  the  distribution  by  groups  of  ten  with  totals  and 
medians.     Fig.  2^,  and  Fig.  24  show  graphically  the  distribution 


78         Spelling  Ability — Its  Measurement  and  DisirihiUion 

for  the  4th  and  5th  grades.     Fig.  8,  Fig.  9,  and  Fig.  10  (page 
33)  give  the  same  for  6th,  7th,  and  8th  grades. 

These  medians  indicate  a  performance  for  these  schools  poorer 
than  Rice  indicates  for  most  of  his  schools  and  much  poorer  than 
Cornman's  results  for  the  two  schools  which  he  tested.  We  can- 
not account  for  this  because  neither  of  these  investigators  tells 
how  he  rated  the  pupils'  papers.  In  our  own  testing  omitted  and 
illegible  words  were  counted  as  wrong.  It  is  probable  that  the 
manner  in  which  Rice  chose  his  schools  would  give  him  those  in 
which  better  than  average  work  was  being  done ;  while  Cornman's 
two  schools  were  without  doubt  devoting  an  unusual  amount  of 
attention  to  spelling  under  his  personal  guidance.  Such  being 
the  case,  it  is  quite  possible  that  the  results  here  given  more 
nearly  approach  typical  conditions,  than  do  those  of  either  of 
these  writers. 

TABLE  XXXI 

Per  Cent  Correct  for  Each  Word  in  Each  Grade  with  Corres- 
ponding P.E.  Values.  Rice  Sentence  Test.  See  Fig.  25 


No.  of 
Word 


3 
4 
5 

6 

7 

8 

9 

10 

11 
12 
13 
14 
15 

10 
17 
18 
19 
20 

21 
22 
23 
24 
25 

26 
27 
2S 
29 
30 


Word 


running  .  . . 
slipped.  .  .  . 
listened  .  .  . 

queer 

speech  .... 

believe.  .  •  . 
weather . .  . 
changeable, 
whistling  . . 
frightened  . 

always . . . . 
changing  .  . 

chain 

loo.se 

baking  . .  .  . 

piece 

receive.  .  .  . 
laughter. .  . 
distance.  .  . 
choose  .  .  . . 

strange. . .  . 
picture.  .  .  . 
because  .  .  . 
thought . .  . 
purpose .  . . 

learn 

lose 

almanac. .  . 
neighbor.. . 
writing. .  .  . 


4th  Grade       5th  Grade       6th  Grade        7th  Grade 


% 


48.0 
30.0 
29.6 
56.9 
45.3 

37.2 
70.9 
27.7 
27.3 
17.8 

53.8 
58.5 
51.8 
24.7 
63.4 

58.5 
21.1 
.59.9 
35.6 
41.7 

57.7 
69.6 
66.2 
58.7 
21.7 

70.6 
46. 4 
10.1 
27.5 
56.3 


P.E. 


+  .074 

+  .777 

+  .794 

—  .258 
+  .175 

+    .484 

—  .816 
+  .878 
+  .895 
+  1.368 

—  .141 

—  .318 

—  .067 
+  1.014 

—  .508 

—  .318 
+  1.191 

—  .372 
+  .547 
+    .311 

—  .2SS 

—  .761 

—  .620 

—  .326 
+ 1 . 160 

—  .803 
+  .134 
+ 1 , 892 
+    .886 

—  .235 


% 


66.0 
34.8 
40.4 
58.8 
41.4 

49.7 
57.5 
31.3 
40.0 
42.7 

68.8 
09.2 
59.8 
49.1 

75.7 

62 

51.7 

71.4 

67.2 

46.3 

74.2 
87.5 
83.9 
72.4 
47.3 

84.9 
.53.1 
21.5 
06.6 
74.0 


P.E. 


—  .612 
+  .579 
+  .360 

—  .330 
+  .322 

+  .011 

—  .280 
+  .723 
+  .376 
+  .273 

—  .727 

—  .744 

—  .368 
+  .0.33 
—1.033 

—  .461 

—  .063 

—  .838 

—  .660 
+  .138 

—  .963 
— 1 . 706 
—1.459 

—  .882 
+    .100 

—1.531 

—  .119 
+  1.170 

—  .6.36 

—  .954 


% 


76.8 
42.9 
53 . 5 
77.3 
72.0 

64.4 
82.8 
46.7 
49.0 
55.6 

78.5 
74.5 
75.3 
45.2 
83.6 

69.9 
59.8 
75.5 
75.8 
56.8 

80 . 9 
94.4 


66.9 

93.2 
.')0.S 
38.6 
65.2 


P.E. 


—1.086 
+    .265 

—  .130 
1.110 

.864 

—  .547 
— 1 . 403 
+  .123 
+    .037 

—  .209 

—1.170 

—  .974 
—1.014 
+  .179 
—1.450 

—  .773 

—  .368 
—1.024 
— 1 . 038 

—  .254 

— 1 . 663 
—2.357 


—  .648 

—2.211 

—  .254 
+    .4.30 

—  .579 


% 


85.0 
51.8 
69.8 
79.0 
77.1 

62.1 
88.0 
66.8 
68. 7 
71.4 

88.6 
89.6 
88. 0 
63.2 
93.5 

83.7 
62.1 
88.8 
88.0 
83.1 

93.5 
97.5 


74.7 

95 . 9 
60.0 
58,6 
85.0 


P.E. 


-1 .  537 

-  .067 

-  .769 
-1.196 
-1.101 

-  .457 
-1.742 

-  .604 

-  .723 

-  .838 

-1.788 
-1.867 
-1 . 742 

-  .500 
-2 . 245 

-1.4.56 

-  .457 
-1.803 
-1.742 
-1.421 

-2 . 245 
-2 . 905 


—   .986 


—2 .  579 
—   .370 


Sth  Grade 


% 


93.4 
70.9 
86.9 
87.3 
80.7 

76.6 
92.2 
65.6 
74.2 
85.7 

95.5 
91.4 
95.9 
81.6 
97.5 

90.6 
80.7 
96.3 
97.5 

85.7 

92.6 
98.8 


92.6 


99.6 
55.7 


-    .322  72.1 
-1.537  93.4 


P.E. 


-2 .  234 

-  .816 
-1.663 
-1.692 
-1.286 

-1.076 
-2.103 

-  .596 

-  .963 
-1.582 

-2.514 
-2 .  035 
-2.579 
-1.335 
-2.905 

-1 , 953 
-1 . 286 
-2.648 
-2.905 
-1 . 582 

-2.145 
-3.346 


-2.145 

-3.938 

-  .213 

-  .869 
-2.234 


Rice  Sentence  Test.     Easy  jo-Word  Test 


79 


TABLE  XXXI 

(Continued) 


No.    of 
Word 


31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

66 
67 
68 
69 

70 

71 
72 
73 
74 
75 

76 
77 
78 
79 
80 

81 
82 
83 
84 
85 
86 


Word 


language .  . 
careful . .  .  . 
enough .... 
necessary. . 
waiting. . . . 

disappoint . 

often 

covered  .  .  . 
mixture . .  . 
getting. .  .  . 

better 

feather. .  .  . 

light 

deceive. . . . 
driving. . .  . 

surface. .  .  . 

rough 

smooth. . . . 
hopping.  .  . 
certainly .  . 

grateful .  . . 
elegant. . .  . 
present. . .  . 
patience. .  . 
succeed .  .  . 

severe 

accident. .  • 
sometimes, 
sensible .  .  . 
business. .  . 


40.3 
54.3 
54.9 
4.5 
55.9 

11.7 
51.6 
42.1 
33.6 
57.5 

80.6 
77.1 
77.5 
18.4 
59.7 

48.4 
64.2 
47.2 
58.1 
16.8 


answer 

sweeping  .  . . 
properly.  .  .  . 
improvement 
fatiguing  .  .  . 

anxious  .  .  . . 
appreciate.  . 

a.ssure 

imagine  .  . .  . 
peculiar  . .  .  . 

character.  .  . 
guarantee. .. 
appro vnl  .  .  . 
intelligent  .  . 
experience. . 


delicious. . . 
realize .... 
importance 
occasion. .  . 
exceptions. 


thoroughly, 
conscientiou' 
therefore  .  . , 
ascending .. 

praise 

wholesome. 


4th  Grade 


% 


P.E. 


+    .364 

—  .160 

—  .183 
+  2.514 

—  .220 

+  1.757 

—  .059 
+  .296 
+    .628 

—  .280 

—1.279 
—1.101 
—1.120 
+  1.335 

—  .364 

+    .059 

—  .539 
+    .104 

—  .303 
+  1.427 


5th  Grade 


% 


62.8 
58.6 
68.0 
21.5 
66.8 

27.4 
57.5 
62.6 
62.6 
74.4 

91.8 
84.1 
90.5 
46.3 
77.1 

79.1 
69.8 
51.3 
oS.l 
36.0 


P.E. 


—  .484 

—  .322 

—  .693 
+  1.170 

—  .604 

.891 
.280 
.476 

—  .476 

—  .972 

—2.064 
—1.481 
— 1 . 944 
+  .138 
—1.101 

—1.201 

—  .769 

—  .048 

—  .303 
+    .531 


6th  Grade 

7th  Grade 

8th  Grade 

% 

P.E. 

% 

P.E. 

% 

P.E. 

68.9 

—   .731 

85.8 

—1.589 

88.1 

—1.749 

SO. 3 

—1.264 

91.0 

—1.988 

98.4 

—3.182 

42.7 

+    .273 

37.6 

+    .468 

61.5 

—   .434 

82.3 

—1.374 

89.9 

—1.892 

92.2 

—2.103 

34.6 

+    .588 

32.4 

+    .657 

38.9 

+    .418 

75.8 

—1.038 

87.2 

—1.685 

92.2 

—2.103 

77.5 

—1.120 

90.2 

—1.918 

97.1 

—2.811 

83.3 

— 1 . 432 

91.0 

-1.988 

97.1 

—2.811 

87.4 

-1.699 

94.6 

—2.384 

97.5 

—2.905 

94.9 

—2.425 

98.6 

—3.258 

100.0 

? 

53.5 

—   .130 

54.8 

—   .179 

79.5 

—1.222 

88.1 

—1.749 

65.7 

—2.177 

98.8 

—3.346 

68.4 

—   .710 

81.2 

—1.313 

89.3 

— 1 . 843 

57.1 

—   .265 

79.0 

—1.196 

91.0 

— 1 . 988 

39.1 

+    .410 

58.6 

—   .322 

61.9 

—  .449 

53 . 5 

—   .130 

65.7 

—    .600 

69.3 

—   .748 

69.7 

—   .765 

79.0 

—1.196 

91.4 

—2.035 

43.4 

+    .246 

63.0 

—    .492 

SO.  7 

—1.286 

53.0 

—   .112 

70.8 

—    .812 

80.7 

—1.286 

40.9 

+    .341 

61.3 

—   .426 

70.9 

— .   816 

45. 5 

+    .168 

68.9 

—   .731 

85.2 

—1.549 

52.5 

—   .093 

67.3 

—   .665 

82.8 

—  1.403 

34.3 

+    .600 

55.0 

—   .187 

65.2 

—   .579 

46.0 

+    .149 

53.7 

—   .138 

68.4 

—   .710 

74.0 

—   .954 

86.9 

— 1 . 663 

93.4 

—2.234 

S7.4 

—1.699 

92.1 

—2.093 

94.7 

—2.397 

61.] 

—   .418 

73.0 

—   .909 

86.5 

—1.636 

59.6 

—   .360 

69.5 

—   .  756 

86.5 

—1.636 

12.6 

+  1.699 

25.3 

+    .986 

31.1 

+    .731 

49.0 

+    .037 

66.2 

—   .620 

84.0 

—1.475 

31.8 

+    .702 

49.0 

+    .037 

74.6 

—   .982 

58.1 

—   .303 

68.9 

—   .731 

86.1 

—1 .  609 

33.6 

+    .628 

47.7 

+    .085 

66.4 

—   .628 

24.0 

+  1.047 

46.3 

+    .138 

56.1 

—   .228 

40.2 

+    ..368 

47.1 

+    .108 

78.7 

—1.181 

11.6 

+  1.772 

19.9 

+  1.253 

25.8 

+    .963 

3S.1 

+    .449 

.56.9 

—1.258 

75.4 

—1.019 

37.1 

+    .448 

43.6 

+    .239 

50.4 

—   .015 

44.4 

+    .209 

63.5 

—   .512 

68.9 

—   .731 

31.3 

+    .723 

61.6 

—   .437 

85.2 

—1 .  549 

53.5 

—   .130 

65.7 

—   .600 

73.4 

—   .927 

47.5 

+    .093173.3 

—   .922 

81.6 

—1 .  335 

34.  S 

+    .579 

44.4 

+    .209 

49.6 

+    .015 

48.2 

+    .067 

57.2 

—   .269 

76.2 

—  1.057 

18.7 

+  1.318 

31.1 

+    .731 

53 . 3 

—    .123 

.3 

+  4.167 

1.6 

+  3.171 

19.7 

+  1.264 

36.4 

+    .516 

62.4 

—   .4RS 

79,9 

—  1.243 

37.6 

+    .468 

.52.0 

—    .074 

55 . 7 

—    .213 

69.0 

—   .735 

78.2 

—1.1.55 

95.9 

—2.579 

56.3 

—    .235 

74.7 

—   .986 

86.1 

—1.609 

8o         Spelling  Ability — Its  Measurement  and  Distribution 

With  respect  to  the  ratings  of  words,  Table  XXXI  gives  for 
each  grade  the  per  cent  of  correct  spellings  and  the  P.E.  values 
calculated  from  the  grade  medians,  assuming  a  normal  distribu- 
tion. Fig.  25  (insert)  shows  the  lines  the  same  words  arranged 
on  a  linear  scale  for  grades  4,  5,  6,  7,  and  8.  Above  the  lines 
the  arrangement  of  the  words  of  the  Preferred  List  is  given.  This 
latter  is  a  repetition  of  the  scales  of  Figures  15,  16,  17,  18  and 
19  (p.  44).  It  will  at  once  be  seen  that  the  former  scales, 
obtained  by  using  the  Preferred  List,  have  been  filled  in  and  have 
been  extended  much  further  to  the  right. 

Just  as  the  more  difficult  words  of  the  Rice  Test  may  be  used 
to  extend  the  scales  to  the  right,  so  the  easier  words  of  the  Easy 
50- Word  Test  may  be  used  to  extend  it  towards  the  left  in  certain 
grades.  In  the  grades  of  the  second  school  year  the  latter  were 
the  only  words  used.  Although  the  primary  object  in  giving  the 
Easy  50- Word  Test  was  to  enable  us  to  give  a  position  to  the 
zero-point,  and  although  for  this  purpose  the  ratings  of  individual 
pupils  were  sufficient,  nevertheless  the  per  cent  of  correct  spellings 
for  each  word  in  each  grade  (2a,  2b,  3d,  and  4th)  was  also 
calculated. 

Table  XXXII  gives  these  per  cents  and  the  corresponding  P.E. 
values.  It  will  be  noted  that  there  are  six  words  (even,  only, 
pretty,  sure,  touch,  and  front)  that  are  common  to  this  list  and 
to  the  Preferred  List. 

TABLE  XXXII 

Per  Cent  Correct  for  Each  Word  in  Each  Grade  with  Corres- 
ponding P.E.  Values.     Easy  50-word  Test 


No. 

of 

Word 

Word 

2a  Grade 
175  Pupils 

2b  Grade 
169  Pupils 

3d  Grade 
168  Pupils 

4th  Grade 
316  Pupils 

% 

P.E. 

% 

P.E. 

% 

P.E. 

% 

P.E. 

1 
2 
3 
4 
5 

6 

7 

8 

9 

10 

you 

will 

hear 

him 

coming . . 

he 

is 

on 

the 

road  .... 

52.6 
46.9 
37.1 
25.7 
9.7 

62.3 
65.7 
57.7 
65.7 
4.6 

—  .097 
+    .119 
+    .489 
+    .968 
+  1.926 

—  .464 

—  .600 

—  .288 

—  .600 
+  2.498 

71.6 
83.4 
53.3 
71.6 
33.7 

88.7 
94,7 
88.7 
94.7 
20.7 

—  .847 
— 1 . 438 

—  .123 

—  .847 
+    .624 

— 1 . 795 
—2.397 
— 1 . 795 
—2 .  397 
+  1,211 

83,9 
96.4 
60.1 
81.0 
57.1 

98.2 
96.4 
94.0 
94.6 
53.6 

—1.459 
—2 .  667 

—  .380 
— 1 . 302 

—  .265 

—3.111 
—2.667 
—2 .  384 
—2.384 

—  .134 

93.4 
99.1 
79,4 
97,5 
83,5 

99,7 
98.4 
97.8 
97.8 
82.6 

—2.234 
—3.506 
—1.217 
—2.905 
— 1 . 444 

—4.083 
—3,182 
—2,986 
—2.986 
—1.391 

4^60       ^  80       <  100      '/20      i  j'-fO      *IL0      ^/SO     *  2Q0 


/«         v^  2»      *7  J4  ^  jj  jf  27  A     -^ 


ovA 


rL\sv 


\5"    tacYCkAe 


Jo  2  8  3t  28 


^    GcrftAe. 


Vh^'  fl"^*^'  "^'^  '"  *'  ^  ^ 


7      tJ^vn-cLc 


3l    »i 


S      &rvcv.i-je^ 


82 


Easy  5o-\Vnrcl  List,    Table   XXXTT.     These  scales  are  not  absolutelj' 
of   the   Rice   List   at   -j-^ij.     I'or  the    lists  referred  to  see  Appendix  II. 


-3ga     -3(,n     -JW     -J2n       -iOO     -280        240     -2*0     -220       200        161)        /(n     -  i>tO     -  lio    -  lao      -go         (,0        -W        -20  O        -20      t^O       »  60       'SO       '100     ■120      i/VO      •It.O      'ISO    •200 


?..v...^-L>.v 


Tw^u-..»."Lv»v  - 


Rice  Sentence  Test.     Easy  jo-Word  Test 


8i 


TABLE  XXXII 

(Continued) 


No. 

of 

Word 


Word 


11 
12 
13 

14 
15 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

26 

27 
28 
29 
30 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 


and 

almost . . . 

sure 

to 

pass 

in 

front .  .  .  . 

of 

me 

I 

send  .  .  .  . 

for 

every 

day 

go 

into 

school.  .  . 

but 

do 

not 

touch .  .  . 

table 

also 

has 

only 

one 

pair 

shoes. .  .  . 

they 

are 

at 

all 

pretty. .  . 

no 

man 

ought . . . 
steal .  .  . . 
even .  .  . . 

a 

penny . . . 


2a  Grade 
175  Pupils 


51.4 
.6 

1.1 
48.0 

1.1 

45.7 
12.0 
25.7 
54.3 
45.1 

22.3 
34.3 
3.4 
36.6 
45.1 

34.3 
16.0 
13.1 
40.1 

33.7 

.6 

1.7 

2.9 

36.0 

5.7 

34.9 

2,9 

1.7 

16.6 

18.3 

43.4 
36.6 
2.9 
23.4 
50.9 

1.1 
1.7 
5.1 
60.6 
3.4 


P.E. 


—  .052 
+  3.725 
+  3.392 
+  .074 
+  3.392 

+  .160 
+  1.742 
+    .968 

—  .160 
+    .183 

+  1.130 
+  .600 
+2.706 
+  .508 
+    .183 

+  .600 
+  1.475 
+  2.767 
+  .372 
+    .624 

+  3.725 
+  3.146 
+  2.811 
+  .531 
+  2.344 

+  .575 
+  2.811 
+  3.146 
+  1.438 
+ 1 . 340 

+  .246 
+  .508 
+  2.811 
+  1.076 

—  .033 

+  3.392 
+  3.146 

+  2.425 

—  .399 
+2.706 


26  Grade 
169  Pupils 


% 


85.2 
6.5 
5.9 

78.7 
27.8 

91.1 

27.8 
64.5 
84.6 
93.5 

25.4 
78.7 
39.6 
89.3 
87.0 

71.0 
60.4 
58.0 
74.0 
69.2 

4.7 
13.0 
15.4 
65.1 
16.6 

71.0 
11.2 
18.9 
34.3 
58.0 

72.8 
62.1 
20.1 
71.0 
74.0 

12.4 
12.4 
24.3 

72.8 
13.6 


P.E. 


—1 .  549 
+2.245 
+  2.321 
—1.181 

+    .873 

—1 .  997 
+    .873 

—  .551 
—1.512 
—2.245 

+  .982 
—1.181 
+  .391 
—1 .  843 
—1.670 

—  .820 

—  .371 

—  .299 

—  .954 

—  .744 

+2.483 
+ 1 . 670 
+  1.512 

—  .575 
+  1.438 

—  .820 
+  1.803 
+  1.307 
+    .600 

—  .299 

—  .900 

—  .457 
+  1.243 

—  .820 

—  .954 

+  1.713 
+  1.713 
+ 1 . 033 

—  .900 
+ 1 . 629 


3d  Grade 
168  Pupils 


% 


P.E. 


97.0— 2. 789 
42.9  +  .265 
48.8  +  .044 
93.5,-2.245 
51.2—   .044 


92.9 
48.2 
82.1 
88.7 
95.2 

48.2 
93.5 
66.7 
94.0 
89,3 

76.2 
81.5 
83.3 
85.1 
86.9 

29.8 
53.6 
35.7 
69.6 
53.0 

82.1 
42.9 
46.4 
64.3 

84.5 

75.0 
73.2 
43.5 
85.1 
79.8 

20.8 
29.8 
48.8 
86.3 
35.7 


—2.177 
+  .067 
— 1 . 363 
— 1 . 795 
—2.468 

+    .067 

—2.245 

—  .640 
—2.305 
— 1 . 843 

—1.057 
— 1 . 329 
— 1 . 432 
— 1 . 543 
—1.663 

+  .786 

—  .239 
+  .543 

—  .761 

—  .112 

—1.363 

+  .265 
+    .134 

—  .543 
— 1 . 506 

—1.000 

—  .918 
+    .243 

— 1 . 543 
—1.238 

+  1.206 
+  .786 
+  .044 
— 1 . 622 
+    .543 


4th  Grafle 
316  PudILs 


% 

P.E. 

98.4 

—3.182 

56.3 

—  .235 

61.1 

—  .418 

94,9 

—2.425 

65,8 

—  .603 

93.0 

—2.188 

67.1 

—  .656 

91.5 

—2.035 

95.9 

—2.579 

00.0 

? 

76.6 

—1.076 

96.8 

—2.746 

88.0 

— 1 . 742 

00.0 

? 

98.1 

—3.077 

89.9 

— 1 . 892 

92,7 

—2.155 

98.4 

—3.182 

97.2 

—2.155 

96.8 

—2.746 

54.4 

—  .164 

94.3 

—2.344 

68.4 

—  .710 

91.5 

—2.035 

70.6 

—  .803 

94.6 

—2  384 

77.5 

— 1 . 120 

76.9 

—1.091 

88.0 

— 1 . 742 

95.9 

—2.579 

86.7 

—1.649 

90.2 

—1.918 

78.5 

—1.170 

96,5 

—2.686 

97,2 

—2.155 

53.8 

—  .141 

67.1 

—  .656 

67.4 

—  .669 

98.4 

—3.182 

63,6 

—  .516 

82         spelling  Ability — Its  Measurement  and  Distribution 

Figures  26,  27,  and  28  give  the  scales  for  these  words.  In 
Figure  27  it  is  indicated  below  the  line  with  the  omission  of  the 
six  words  noted  in  the  last  paragraph.  Above  the  line  the 
words  of  the  Preferred  List  are  reproduced  from  Figure  14. 
Since  the  Easy  50-Word  Test  was  also  given  to  4th-grade  chil- 
dren it  is  likewise  scaled  for  that  grade  omitting  the  same  six 
words.     (Fig.  25,  4th  grade,  lower  line.) 

We  have,  therefore,  scales  for  every  grade  from  the  first  half 
of  the  second  grade  to  and  including  the  eighth.  All  of  these 
scales  above  the  2d  grade  are  much  richer  than  were  those 
given  in  Section  12.  There  are  fewer  gaps  in  them  and  their 
range  is  greater.  They  may  be  used  to  great  advantage  in 
testing  the  spelling  ability  of  children  in  any  grade  of  the 
elementary  school  in  which  children  are  supposed  to  have  any 
such  ability.  If  it  is  not  convenient  to  use  a  whole  scale,  certain 
words  differing  in  difficulty  by  approximately  equal  amounts 
may  be  selected.  Groups  of  words  may  be  made  each  of  equal 
difficulty  as  a  group,  or  each  differing  from  the  preceding  group 
by  a  fixed  amount.  The  position  of  each  word  shows  the  weight 
which  ought  to  be  assigned  to  it  for  test  purposes. 

Each  of  these  grade  scales  refers  to  the  median  of  the  grade 
as  the  zero-point.  In  Figure  29  is  shown  a  scale  for  all  grades 
referring,  as  in  Figure  20,  to  the  median  of  the  3d  grade  as  the 
zero-point.  Above  the  line  is  shown  the  Preferred  List  as  in 
Fig  20.  Below  it  are  arranged  the  words  of  Rice's  Test;  and 
on  a  parallel  scale  the  Easy  50-Word  List.  Caution,  however, 
ought  to  be  observed  in  accepting  too  literally  the  showing  of 
the  last  two  lists.  Rice's  Test  was  not  given  to  the  3d  grade, 
and  the  Easy  50-Word  Test  was  given  to  the  2d  grade  and 
was  not  given  above  the  4th.  They  cannot,  therefore,  be  closely 
compared  with  the  Preferred  List.  The  effect  of  high  grades 
is  to  make  the  words  harder,  of  low  grades  to  make  them  easier. 
In  the  case  of  the  Rice  Test  the  words  are  probably  a  little — 
but  only  a  little — too  far  to  the  right, —  i.e.,  farther  toward  the 
high  end  than  they  would  have  been  had  they  been  used  in  the 
3d  grade — as  Cornman  used  them.  In  the  case  of  the  Easy 
50- Word  Test  the  words  would  be  a  great  deal  too  far  to  the 
left  if  set  down  as  the  record  indicated.    The  six  words  common 


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Rice  Sentence  Test.     Easy  50-Word  Test  83 

to  this  list  and  to  the  Preferred  List  enable  us  to  suggest  a 
correction.  Their  P.E.  values,  when  the  averages  of  the  grades 
writing  them  are  taken,  appear  as  follows : 

Easy  50-  Preferred 

word  List                List  Increase 

sure +.530  +1.57  1.04 

front —.299  +1.0G  1.36 

touch +.652  +1.71  1.06 

only —.089  —  .  57  .66 

pretty —.024  +1.31  1.33 

even —.097  +    .70  .80 

Average  Increase     1.04 

It  appears,  therefore,  that  in  order  to  compare  the  words  of 
the  Easy  50-\Vord  List  with  those  of  the  Preferred  List  and 
to  scale  them  together  we  ought  to  raise  all  the  words  of  the 
former  list  about  i  P.E.  In  Figure  29,  accordingly,  all  these 
words  have  been  raised  that  amount. 

Fig.  29  shows  our  most  complete  scale.  It  has  decided  limita- 
tions, and  it  is  impossible — in  the  case  of  the  newly  added 
words — to  suppose  that  it  is  more  than  an  approximation.  A 
great  deal  more  testing  than  we  have  been  able  to  do  will  have 
to  be  done  before  these  words  and  others  with  them  can  be 
precisely  fixed  beyond  dispute.  It  is  not  claimed  that  the  scale 
we  give  is  final.  We  think,  however,  that,  supposing  the  two 
fundamental  assumptions  upon  which  it  is  based  to  be  valid, 
it  may  be  used  in  its  present  form  with  substantially  accurate 
results ;  and  we  are  confident  that  the  general  method  by  which 
it  has  been  derived  is  the  one  by  which  a  final  scale  may  ulti- 
mately be  secured. 

The  top  figures  in  Fig.  29  refer  to  the  absolute  zero-point, 
taken  as  470  below  the  3d-grade  median.  It  enables  us  to  state 
not  only  the  difiference  in  difficulty  between  words  but  their 
relationships.  We  may  say,  for  instance,  that  school  (No.  27 
E.  50-W.  L.,  scales  at  428)  is  one-half  as  hard  as  grateful 
(No.  51  R.  S.  T.,  scales  at  856).  We  may  put  certain  facts  in 
equation  form  as  follows : 

in  =  Yz  light  ==:  y^  pigeons  =  34  fatiguing 

is  =  j4  also  =  Yz  occasion  =  Y  conscientious 

the  =  3/2  chicken  =  Y  approval 

and  =  Yz  penny  =  Y2,  pecxdiar 


84         Spelling  Ability — Its  Measurement  and  Distribution 

Many  more  such  statements  may  be  made.  It  will,  we  think, 
surprise  most  people  to  learn  that  fatiguing  is  only  four  times 
as  hard  as  he,  or  that  to  spell  occasion  shows  but  three  times  as 
much  ability  as  to  spell  is. 

In  fact  it  will,  we  think,  be  seriously  questioned  whether  such 
words  as  at,  of,  on,  do,  etc.,  have  difficulties  anything  like  as 
great  as  is  shown  on  our  scale.  It  will  be  asked,  What  words 
can  be  easier  than  these?  If  a  child  cannot  spell  them  does  he 
not  show  zero  ability?  The  answer  is  that  if  one  or  more  of 
these  very  easy  words  were  isolated  and  pronounced  to  a  group 
to  be  written,  those  who  could  not  spell  them  would  indeed 
show  no  spelling  ability.  But  these  words  were  not  isolated, 
they  were  given  in  a  context.  It  is  one  thing  for  children  to 
write  the  word  "  at "  when  pronounced  alone  or  in  column 
dictation.  It  is  quite  another  to  write  it  in  the  sentence:  *'  They 
are  not  at  all  pretty."  Some  will  omit  it,  and  this  fault  is  not 
confined  by  any  means  to  the  lowest  classes.  Some  will  connect 
it  with  the  word  all.  because  they  habitually  do  so  in  speaking. 
Some  little  children  will  quite  break  down  on  the  whole  sentence 
because  they  can't  get  over  the  word  "  they."  In  other  sentences 
some  will  substitute  a  word  (generally  of  similar  meaning)  for 
the  one  dictated.  Each  of  these  faults  scores  *'  wrong,"  and 
none  of  them  would  be  made  in  column  dictation.  It  is  also  true 
that  children  writing  sentences  more  often  write  illegibly  than 
they  do  when  writing  a  few  words  in  columns ;  and  this  is 
particularly  true  with  young  children. 

It  will  therefore  be  clear  that  the  decision  as  to  how  hard  a 
word  is,  depends  on  how  you  use  it  in  testing  and  when  you  call 
it  "  wrong."  To  verify  the  placings  of  the  words  given  in  this 
study  one  ought  to  use  the  same  test  material  and  the  same 
method  of  scoring.  In  particular,  column  dictation  will  not  do 
at  all. 

§  19.    Derived  Forms  of  Distribution 

The  foregoing  treatment  of  the  measurement  of  spelling 
ability  has,  as  has  been  indicated  frequently,  proceeded  upon 
the  assumption  that  the  distribution  of  ability  is  in  all  grades 
normal.  Such  an  assumption  has  always  been  made  in  the 
investigation  of  school  abilities  by  persons  whose  knowledge  of 


Derived  Forms  of  Distribution  85 

the  theory  of  statistics  has  enabled  them  to  do  so.  In  Section  10 
I  have  said :  "  There  seems  no  good  ground  for  assuming  that 
the  distribution  of  spelHng  ability  in  any  grade  is  not  according 
to  the  normal  curve  or  according  to  a  curve  which  resembles  it 
closely."  liy  this  alternative  is  suggested  the  possible  applica- 
bility of  certain  curves  not  of  normal  form  but  resembling  the 
normal  form.  Our  problem  will  now  be  to  derive  and  apply 
to  some  of  our  material  such  modifications  of  the  type  form  of 
distribution  as  our  present  knowledge  of  grade  conditions 
permits. 

In  order  that  the  frequency  of  measurements  within  a  group 
may  be  distributed  according  to  the  Probability  Integral  it  is 
necessary  that  the  group  be  in  no  way  selected  on  the  basis  of 
the  characteristic  that  is  measured.  It  must  be  a  random 
sampling  from  a  "  total  population."  If  the  frequency  distribu- 
tions of  statures  for  adult  males  born  in  the  City  of  New  York 
may  be  expected  to  approximate  the  symmetrical  type,  the 
distributions  of  statures  for  adult  males  on  the  police  force  of 
New  York  City  would  not  do  so.  Their  curve  will  be  of  the 
"  moderately  asymmetrical  t}'pe  "  being  cut  off  at  the  low  end 
because  extremely  short  men  are  at  a  disadvantage  in  the  group 
supposed  to  be  measured.  In  other  words,  there  is  a  selection 
on  the  basis  of  stature.  The  group  "  adult  males  on  the  police 
force  of  New  York  City  "  is  not  a  random  sampling  of  the  total 
population  "  adult  males  of  New  York  City." 

The  question  then  is :  To  what  extent  does  the  membership 
of  each  grade  of  the  elementary  school  fail  of  being  a  chance 
selection  from  a  total  population  ?  We  may  fairly  assume,  in  the 
first  place,  that  the  pupils  of  the  first  and  second  grades  are 
unselected.  Practically  all  children  attend  school  and  none  drop 
out  in  these  grades.  From  the  3d  grade  on,  however,  each 
successive  grade  constitutes  a  group  which  is  less  and  less  a 
random  sampling.  I\Iany  influences  are  at  w'ork  to  eliminate 
a  greater  and  greater  number  of  individuals.  Probably  the  most 
important  of  them  is  the  inability  of  children  to  progress — i.e., 
lack  of  ability  in  the  lines  of  work  now  required  by  the  schools. 

The  extent  to  w^hich  elimination  takes  place  in  the  grades  has 
been  the  subject  of  study  by  a  number  of  investigators.  The 
first  of  these  was  Thomdike  ('07).    He  draws  conclusions  from 


86         Spelling  Ability — Its  Measurement  and  Distribution 

conditions  in  23  cities  as  they  were  about  1900.  He  estimates 
that  out  of  100  entering  pupils,  97  remain  till  grade  3,  90  till 
grade  4,  81  till  grade  5,  68  till  grade  6,  54  till  grade  7,  and  40 
till  the  last  grammar  grade  (8th  or  9th).  Ayres  ('09)  sharply 
criticised  these  figures,  stating  that  they  were  too  small.  He 
contended,  particularly,  that  there  was  no  dropping  out  before 
the  6th  year — a  conclusion  which  common  observation  and  later 
investigation  unite  to  disprove.  Employment  certificates  are 
granted  in  great  numbers  to  5th-grade  children.  Mr.  Ayres' 
fiigures  for  retention  are  as  follows:  Grades  1-5,  100  (i.e.,  no 
elimination)  ;  grade  6,  90;  grade  7,  71 ;  grade  8,  51. 

Thorndike,  using  later  and  better  reports,  subsequently  derived 
figures  a  little  higher  than  his  former  ones,  but  substantially 
in  agreement  with  them  (Thorndike,  '10).  They  were  no  higher 
probably  than  5  or  6  years  of  agitation  would  have  led  one  to 
expect. 

Another  important  study  of  this  question  was  made  by 
Strayer  ('11),  the  material  being  used  from  318  cities.  His 
conclusions  tend  to  group  with  Thorndike's  rather  than  with 
those  of  Ayres.  Owing  to  the  large  number  of  cities  whose 
returns  were  used,  the  uniform  method  of  taking  the  census, 
and  the  recency  of  the  conditions  studied,  this  investigation  is 
highly  important.  No  single  figures  are  given  for  retention  in 
general,  though  they  are  easily  found.  Using  the  largest  age 
group  as  the  number  of  entering  children,  he  gives  the  following 
as  the  median  per  cents  in  each  grade. 


Cities  of  Over  25,000 

Cities  of  Less  than  25,000 

Boys 

Girls 

Boys 

Girls 

3d   year 

4th     "    

115 

110 

100 

85 

65 

50 

110 
110 
95 
85 
75 
60 

110 

105 
95 
80 
70 
50 

105 
100 

5th     "    

95 

6th     "    

85 

7th     "    

70 

8th     "    

60 

Since  in  this  study  we  group  boys  and  girls  together  and  consider 
general  conditions,  the  average  of  these  percentages  will  give 
figures  for  retention  for  each  grade   (subject  to  deduction  for 


Derived  Forms  of  Distribution 


87 


repeaters)  as  follows:  3d  grade,  no;  4th  grade,  106;  5th  grade, 
96;  6th  grade,  84;  7th  grade,  70;  8th  grade,  55.  If,  as  Dr. 
Strayer  says,  a  fair  estimate  of  the  number  of  repeaters  in  the 
6th,  7th,  and  8th  grades  would  be  12%,  10%,  and  8%  of  the 
pupils  in  each  grade  (p.  136),  it  is  likely  that  the  progression 
(8,  10,  12)  may  be  carried  back  to  the  5th,  4th  and  3d  grades 
without  great  violence  to  the  facts.  We  estimate  therefore  that 
the  number  of  repeaters  in  the  3d,  4th,  and  5th  grades  is  18%, 
16%,  and  14%  of  the  pupils  in  each  grade.  Making  these  de- 
ductions from  the  above  percentages,  we  have  for  the  retention : 
3d  grade,  92 ;  4th  grade,  90 ;  5th  grade,  82 ;  6th  grade,  72 ;  7th 
grade,  60;  8th  grade,  47. 

Weighing  as  best  we  can  the  results  of  these  four  studies, 
we  have  made  the  best  estimate  we  can  for  the  probable  amount 
of  retention  at  present  in  the  grades.  For  reasons  that  will 
appear  later  we  have  expressed  this  estimate  in  numbers  per 
10,000  instead  of  per  100. 

Table  XXXIII  and  Fig.  30  show  the  percentages  we  have 
adopted  compared  with  those  of  Thorndike,  Ayres,  and  Strayer 
(as  derived).  Fig.  30  gives  only  the  earlier  of  Thorndike's 
percentages. 

TABLE  XXXIII 
Percentages  of  Retention.     Grades  3  to  8 


8th 


Thorndike  '07 

Ayres  '09 

Thorndike  '10 

Strayer  '11  (derived) .  . 

Adopted 


3d 

4th 

5th 

6th 

7th 

97 

90 

81 

68 

54 

100 

100 

100 

90 

71 

91 

81.5 

70.9 

56 

92 

90 

82 

72 

60 

97.25 

95.46 

88.40 

70  87 

57.44 

40 
51 
41.2 

47 


48.21 


Such  an  amount  of  retention  for  each  grade  having  been 
adopted,  the  next  question  to  consider  is :  What  part  of  a 
normal  distribution  is  thus  eliminated?  Obviously  not  all  the 
poorest  in  ability  drop  out.  Our  results  for  spelling  show  that 
some  very  poor  spellers  are  retained  even  in  the  highest  grades. 
Yet  the  greatest  elimination  will  no  doubt  be  among  those  of 
lowest  ability  and  will  be  progressively  less  among  children  of 
greater  ability.    How  much  this  amounts  to  for  successive  incre- 


88         Spelling  Ability — Its  Measurement  and  Distribution 

merits  of  ability  we  do  not  positively  know.  We  are  again  forced 
to  make  as  reasonable  an  estimate  as  we  can,  and  this  time 
without  the  help  of  any  investigations. 


m 

80 

10 

so 

30 


CLfLopted 


.TK£>i-niiKeb7 
5tra\je-r  (^cvrtVi^  estimated) 


Fig.  30.     The  horizontal  scale  is  for  the  grades  of  the  elementary  school ; 
the  vertical  scale  is  for  percentage  of  pupils  retained. 

We  have  estimated  (Table  XXXIII)  that  9725  out  of  10,000  en- 
tering children  are  retained  in  the  3d  grade;  and  we  judge  further 
that  all  below  — 4  P.E.  have  dropped  out,  that  at  —  3  P.E.  40% 
have  drppped  out,  and  that  at  — 2  P.E.  none  at  all.  In  the  4th 
grade,  retention  is  put  at  9546  in  10,000  (Table  XXXIII)  and 
total  elimination  is  estimated  to  operate  up  to —  3.7  P.E.  From  this 
point  to  —  2.7  P.E.  the  force  of  elimination  is  supposed  gradually 
to  diminish  until  40%  drop  out.  At  —  1.7  P.E.  only  10%  are 
estimated  as  lost  to  the  grade.  At  —  1.2  P.E.  the  forces  tending 
to  eliminate  children  are  supposed  to  have  been  completely 
counteracted  by  the  opposing  forces  tending  to  retain  them.  In 
the  5th  grade  (8840  out  of  10,000  retained)  the  elimination  is 


Derived  Forms  of  Distribution 


89 


assumed  to  be  total  up  to  —  3.2  P.E.  and  partial  as  high  as 
—  0.2  P.E.  In  the  6th  grade  (7087  out  of  10,000  retained)  the 
corresponding  points  are  —  2.7  P.E.  and  +  3.3  P.E. ;  in  the  7th 
(5744  retained)  they  are  — 2.3  P.E.  and  +  3.7  P.E. ;  and  in  the 
8th  (4821  retained),  —  2  P.E.  and  +  6  P.E.  It  is,  therefore,  sup- 
posed that  in  the  last  three  years  of  the  elementary  school  there 
is  some  elimination  even  among  the  most  capable  children.  This 
plan  of  elimination  and  retention  may  easily  be  attacked  as 
artificial  and  it  may  very  likely  be  shown  to  need  considerable 
modification  when  later  and  better  knowledge  is  available  on  this 
difficult  subject.  Meanwhile,  however,  some  assumption  was 
necessary  in  order  to  construct  any  sort  of  frequency  tables 
which  should  illustrate  the  method  of  constructing  a  scale  when 
account  is  taken  of  the  selective  influence  of  the  grades.  We  can 
only  state  that  we  have  keenly  appreciated  the  importance  of 
distributing  the  amount  of  elimination  where  it  most  probably 
occurs,  that  we  have  been  at  no  small  pains  to  find  out  where 
to  distribute  it,  and  that  we  have  estimated  as  wisely  as  we  could. 
Table  XXXIV  gives  the  entire  plan  of  elimination  and  retention 

for  each  grade. 

^  TABLE  XXXIV 

Plan  of  Elimination  and  Retention  for  Each  Grade 


tX 

Per 

Per 

X 

Per 

Per 

Grade,  etc. 

cent 

cent 

Grade,  etc. 

cent 

cent 

P.E. 

eliminated 

retained 

P.E. 

eliminated 

retained 

3d  Grade. 

—4 

100 

0 

7th  Grade 

—2.3 

100 

0 

iV=9725  . 

—3 

40 

60 

A^==5744  . 

—1.3 

70 

30 

2 

0 

100 

—0.3 

+  0.7 

50 
20 

50 
80 

4th  Grade 

—3.7 

100 

0 

+  1.7 

10 

90 

A'=0546  . 

—2.7 

40 

60 

+  2.7 

5 

95 

—1.7 

10 

90 

+  3.7 

0 

100 

—1.2 

0 

100 

8th  Grade 

Ar=4821  . 

0 

100 
70 

0 
30 

5th  Grade 

—3.2 

100 

0 

—1 

N=SMO  . 

—2.2 

50 

50 

0 

50 

50 

—1.2 

20 

SO 

+  1 

30 

70 

—0.2 

0 

100 

+  2 
+  3 

+  4 

20 

10 

6 

80 
90 
94 

6th  Grade 

—2.7 

100 

0 

iV=7087  . 

—1.7 

60 

40 

+  5 

2 

98 

—0.7 

35 

65 

+  6 

0 

100 

+  0.3 

15 

85 

+  1.3 

10 

90 

+  2.3 

5 

95 

+  3.3 

0 

100 

go         Spelling  Ability — Its  Measurement  and  Distribution 


-^F£     -Jf&    -2?i    -Ti 


+?i      iZ?i     +3P&,    i^Pd 


Figs.  31-36.     The  estimated  amount  and  distribution   of  elimination  and 
retention.     See  Table  XXXIII. 


Derived  Forms  of  Distribution  9 1 

The  next  step  was  to  apply  the  data  of  Table  XXXIV  to  the 
normal  distribution  and  to  derive  therefrom  for  each  grade  a 
modified  distribution  which  should  take  account  of  the  amount 
and  range  of  elimination  as  estimated.  In  order  that  the  validity 
of  our  method  may  be  open  to  inspection,  we  shall  illustrate  for 
the  6th  grade  the  manner  in  which  these  modified  distributions 
were  derived. 

We  have  adopted  certain  percentages  of  retention  for  desig- 
nated amounts  of  general  ability  (Table  XXXIV,  6th  grade), 
and  these  percentages  must  not  only  stand  the  test  of  reasonable- 
ness in  themselves,  but  they  must  also  when  applied  to  a  normal 
table  of  frequency  (the  sum  of  whose  cases  is,  say,  1000),  reduce 
the  number  of  cases  to  an  amount  which  represents  a  reasonable 
percentage  of  retention  for  the  6th  grade  (say,  70  or  71).  That 
is,  the  derived  table  must  show  approximately  700  cases  out  of 
1000,  or  7000  out  of  10,000.  We  shall  see  later  to  what  extent 
this  turns  out  to  be  true. 

Adapting  the  normal  table  of  frequency  (Table  XIV,  page  35) 
so  as  to  include  1000  cases  instead  of  10,000  and  taking  intervals 
of  o.i  P.E.,  we  have  columns  i  and  2  of  Table  XXXV.  In 
column  3  we  increase  the  percentages  of  retention  from  o  at 

—  2.7  P.E.  to  40  at  —  1.7  P.E.  by  increments  of  4  for  each  of  the 
ten  steps ;  then  by  increments  of  2.5  until  65   is   reached   at 

—  0.7  P.E. ;  then  by  increments  of  2  to  85  at  +  0.3  P.E. ;  and 
so  on  as  required  by  Table  XXXIV,  col.  4.  Taking  these 
percentages  of  the  frequencies  in  column  2  gives  the  derived 
frequencies  of  column  4.  The  sum  of  the  entries  in  this  column 
being  708.7,  the  plan  gives  an  amount  of  elimination  which  is 
reasonable  for  the  6th  grade.     (See  Table  XXXIII.) 

The  amount  and  distribution  of  elimination  and  retention  are 
shown  by  diagram  for  each  grade  in  Figs.  31  to  36.  Fig.  34 
in  particular  shows  these  facts  for  the  6th  grade,  and  is  the 
graphic  representation  of  the  series  of  frequencies  in  column  4 
of  Table  XXXV.  Fig.  31  shows  the  same  facts  for  the  3d 
grade,  Fig.  32  for  the  4th  grade,  etc.  The  progressive  increase 
in  elimination  and  the  extension  of  it  to  higher  and  higher  parts 
of  the  normal  curve  are  the  facts  to  be  noticed. 

But  we  have  not  in  column  4  of  Table  XXXV,  a  frequency 
table  for  the  6th  grade  in  the  most  useful  form.    The  area  of  its 


92 


spelling  Ability — Its  Measurement  and  Distribution 


TABLE  XXXV 

Sixth  Grade.     Derivation  of  Modified  Table  of  Frequency 

Below  Normal  Median  Above  Normal  Median 


Per- 

Per- 

Normal 

cent- 

Derived 

Sanae  on 

Normal 

cent 

Derived 

Same  on 

X 

Fre- 

ages 

Fre- 

basis of 

X 

Fre- 

ages 

Fre- 

basis of 

quen- 

of 

quen- 

10,000 

quen- 

of 

quen- 

10,000 

P.E. 

cies 

Reten- 
tion 

cies 

cases 

P.E. 

cies 

Reten- 
tion 

cies 

cases 

0—1 

27 

79 

21.3 

301 

0— .1 

27 

81 

21.9 

309 

.2 

27 

77 

20.8 

293 

.2 

27 

83 

22.4 

312 

.3 

26 

75 

19.5 

275 

.3 

26 

5? 

22.1 

316 

.4 

26 

73 

19.0 

268 

.4 

26 

85.5 

22.2 

316 

.5 

26 

71 

18.5 

261 

.5 

26 

86 

22.4 

313 

.6 

25 

69 

17.3 

244 

.6 

25 

86.5 

21.6 

308 

.7 

25 

67 

16.8 

237 

.7 

25 

87 

21.8 

305 

.8 

23 

6^ 

15.0 

212 

.8 

23 

87.5 

20.1 

284 

.9 

23 

62.5 

14.4 

203 

.9 

23 

88 

20.2 

285 

1.0 

22 

60 

13.2 

186 

1.0 

22 

88.5 

19.5 

275 

1.1 

21 

57  5 

12.1 

171 

1.1 

21 

89 

18.7 

264 

1.2 

20 

55 

11.0 

155 

1.2 

20 

89.5 

17.9 

252 

1.3 

19 

52.5 

10.0 

141 

1.3 

19 

90 

17.1 

241 

1.4 

18 

50 

9.0 

127 

1.4 

18 

90.5 

16.3 

230 

1.5 

16 

47.5 

7.6 

107 

1.5 

16 

91 

14.6 

206 

1.6 

16 

45 

7.2 

102 

1.6 

16 

91.5 

14.6 

206 

1.7 

14 

42.5 

6.0 

85 

1.7 

14 

92 

12.9 

182 

1.8 

14 

40 

5.6 

79 

1.8 

14 

92.5 

13.0 

183 

1.9 

12 

36 

4.3 

61 

1.9 

12 

93 

11.2 

158 

2.0 

11 

32 

3.5 

50 

2.0 

11 

93.5 

10.3 

145 

2.1 

11 

28 

3.1 

44 

2.1 

11 

94 

10.3 

145 

2.2 

9 

24 

2.2 

31 

2.2 

9 

94.5 

8.5 

121 

2.3 

9 

20 

1.8 

26 

2.3 

9 

05 

8.6 

120 

2.4 

7 

16 

1.1 

16 

2.4 

7 

95.5 

6.7 

95 

2.5 

7 

12 

8 

11 

2.5 

7 

96 

6.7 

95 

2.6 

6 

8 

.5 

7 

2.6 

6 

96.5 

5.8 

82 

2.7 

6 

4 

.2 

3 

2.7 

6 

97 

5.8 

82 

2.8 

5 

0 

0 

0 

2.8 

5 

97.5 

4.9 

69 

2.9 

4 

98 

3.9 

55 

3.0 

4 

98.5 

3.9 

55 

3.1 

3 

99 

3.0 

42 

3.2 

3 

99.5 

3.0 

42 

3.3 

2 

100 

2.0 

28 

3.4 

2 

100 

2.0 

28 

3.5 

2 

100 

2.0 

28 

3.6 

2 

100 

2.0 

28 

3.7 

1 

100 

1.0 

14 

3.8 

1 

100 

1.0 

14 

3.9 

1 

100 

1.0 

14 

4.0 

1 

100 

1.0 

14 

etc.  to 

etc.  to 

etc. 

etc.  to 

etc.  to 

tal  No. 

cases. . 

6.0 

.02 

.02 

.28 

To 

1000 

708.7 

9999.72 

Derived  Forms  of  Distribution 


93 


curve  is  no  longer  looo,  but  only  708.7.  In  order  to  express  the 
several  frequencies  in  the  form  of  per  cents,  we  shall  have  to 
divide  each  of  them  (column  4)  by  their  total  (708.7).  Express- 
ing these  quotients  on  the  basis  of  10,000  instead  of  1000,  w^e  have 
column  5.  These  are  the  numbers  in  the  columns  3  and  5  of 
Table  XXXIX  (p.  96)  ;  and  when  their  sums  are  taken  begin- 
ning at  o  they  constitute  the  Modified  Table  of  Frequency  for 
the  6th  grade  (Table  XXXIX). 


TABLE  XXXVI 
Modified  Table  of  Frequency,  3d  Grade.     Median  =4-0.051  P.E. 
Plan  of  elimination:    —4   P.E.,    100%;  —3    P.E.,   40%;   —2  P.E.,  0% , 
Total  area  of  the  surface  of  frequency  taken  as  10,000.     See  Fig.  37. 


X 

Lo 

w 

Hi 

gh 

X 

P.E. 

Low 

High 

X 

P.E. 

Low 

High 

P.E. 

% 

A 

% 

A 

% 

A 

% 

A 

% 

A 

% 

A 

278 

278 

109 

113 

5.1 

.1 

278 

278 

278 

278 

2.1 

4334 

85 

4338 

93 

4.1 

5116.1 

5.1 

.2 

556 

267 

556 

267 

2.2 

4419 

81 

4431 

93 

4.2 

5121.2 

5.1 

.3 

823 

267 

823 

267 

2.3 

4500 

60 

4524 

72 

4.3 

5126.3 

4.1 

.4 

1090 

267 

1090 

267 

2.4 

4560 

58 

4596 

72 

4.4 

5130.4 

2.1 

.0 

1357 

257 

1357 

257 

2.5 

4618 

47 

4668 

62 

4.5 

5132.5 

2.1 

.6 

1614 

257 

1614 

2.57 

2.6 

4665 

44 

4730 

62 

4.6 

5134.6 

1.0 

.7 

1871 

236 

1871 

236 

2.7 

4709 

35 

4792 

51 

4.7 

5135.6 

1.0 

.8 

2107 

236 

2107 

236 

2.8 

4744 

26 

4843 

41 

4.8 

5136.6 

1.0 

.9 

2343 

226 

2343 

226 

2.9 

4770 

25 

4884 

41 

4.9 

5137.6 

1.0 

1.0 

2569 

216 

2569 

216 

3.0 

4795 

17 

4925 

31 

5.0 

5138.6 

.51 

1.1 

2785 

206 

2785 

206 

3.1 

4812 

15 

4956 

31 

5.1 

5139.11 

,51 

1.2 

2991 

195 

2991 

195 

3.2 

4827 

9 

4987 

21 

5.2 

5139.62 

.31 

1.3 

3186 

185 

3186 

185 

3.3 

4836 

7.4 

5008 

21 

5.3 

5139.93 

.31 

1.4 

3371 

165 

3371 

16) 

3.4 

4843.4 

6.2 

5029 

21 

5.4 

5140.24 

.31 

1.5 

3536 

165 

3536 

165 

3.5 

4849.6 

4.9 

5050 

21 

5.5 

5140.55 

.31 

1.6 

3701 

144 

3701 

144 

3.6 

4854.5 

1.9 

5071 

10 

5.6 

5140.86 

.21 

1.7 

3845 

144 

3845 

144 

3.7 

4856.4 

1.2 

5081 

10 

5.7 

5141.07 

.21 

1.8 

3989 

123 

3989 

123 

3.8 

4857.6 

0.6 

5091 

10 

5.8 

5141.28 

.21 

1.9 

4112 

113 

4112 

113 

3.9 

4858.2 

5101 

10 

5.9 

5141.49 

.21 

2.0 

4225 

4225 

4.0 

5111 

6.0 

5141.70 

94         Spelling  Ability — Its  Measurement  and  Distribution 


TABLE  XXXVII 
Modified  Table  of  Frequency,  4th  Grade.     Median==  + 0.087  P.E. 
Plan  of  elimination:     —3.7  P.E.,  100%;    —2.7  P.E.,  40%;    —1.7  P.E., 
10%;  — 1.2   P.E.,  0%.      Total  area  of  the  surface  of  frequency  taken  as 
10,000.     See  Fig.  38. 


X 

Low 

High 

X 

Low 

High 

X 

Low 

High 

P.E. 

% 

A 

% 

A 

P.E. 

% 

A 

% 

A 

P.E. 

% 

A 

% 

A 

283 

283 

93 

115 

5.2 

.1 

283 

283 

283 

283 

2.1 

4316 

74 

4421 

94 

4.1 

5210.2 

5.2 

.2 

566 

272 

566 

272 

2.2 

4390 

71 

4515 

94 

4.2 

5215.4 

5.2 

.3 

838 

272 

838 

272 

2.3 

4461 

53 

4609 

73 

4.3 

5220.6 

4.2 

.4 

1110 

271 

1110 

271 

2.4 

4514 

51 

4682 

73 

4.4 

5224.8 

2.1 

.5 

1381 

262 

1381 

262 

2.5 

4565 

41 

4755 

63 

4.5 

5226.9 

2.1 

.6 

1643 

262 

1643 

262 

2.6 

4606 

40 

4818 

63 

4.6 

5229 

1.05 

.7 

1905 

241 

1905 

241 

2.7 

4646 

31 

4881 

52 

4.7 

5230.05 

1.05 

.8 

2146 

241 

2146 

241 

2.8 

4677 

23 

4933 

42 

4.8 

5231.10 

1.05 

.9 

2387 

230 

2387 

230 

2.9 

4700 

20 

4975 

42 

4.9 

5232.15 

1.05 

1.0 

2617 

220 

2617 

220 

3.0 

4720 

13 

5017 

31 

5.0 

5233.20 

.52 

1.1 

2837 

210 

2837 

210 

3.1 

4733 

11 

5048 

31 

5.1 

5233.72 

.52 

1.2 

3047 

199 

3047 

199 

3.2 

4744 

6 

5079 

21 

5.2 

5234.24 

.31 

1.3 

3246 

185 

3246 

189 

3.3 

4750 

5 

5100 

21 

5.3 

5234.55 

.31 

1.4 

3431 

161 

3435 

168 

3.4 

4755 

4 

5121 

21 

5.4 

5234.80 

.31 

1.5 

3592 

158 

3603 

168 

3.5 

4759 

3 

5142 

21 

5.5 

5235.17 

.31 

1.6 

3750 

135 

3771 

147 

3.6 

4762 

1 

5163 

10.5 

5.6 

5235.48 

.21 

1.7 

3885 

132 

3918 

147 

3.7 

4763 

5173.5 

10.5 

5.7 

5235.69 

.21 

1.8 

4017 

109 

4065 

126 

3.8 

5184 

10.5 

5.8 

5235.90 

.21 

1.9 

4126 

97 

4191 

115 

3.9 

5194.5 

10.5 

5.9 

5236.11 

.21 

2.0 

4223 

4306 

4.0 

5205 

6.0 

5236.32 

Derived  Forms  of  Distribution 


95 


TABLE  XXXVIII 
Modified  Table  op  Frequency,  5th  Grade.     Median= +0.215  P.E. 
Plan  of  elimination:    —3.2  P.E.,  100%;    —2.2  P.E.,  50%;   —1.2  P.  E., 
20%;    — 0.2  P.E.,  0%.     Total  area  of  the  surface  of  frequency  taken  as 
10,000.     See  Fig.  39. 


X 

Low 

High 

X 

P.E. 

Low 

High 

X 

Low 

High 

P.E. 

% 

A 

% 

A 

% 

A 

% 

A 

P.E. 

% 

A 

% 

A 

305 

305 

70 

124 

6 

.1 

305 

305 

305 

305 

2.1 

4093 

54 

4772 

102 

4.1 

5627 

6 

.2 

610 

294 

610 

294 

2.2 

4147 

51 

4874 

102 

4.2 

5633 

6 

.3 

904 

288 

904 

294 

2.3 

419S 

36 

4976 

79 

4.3 

5639 

5 

.4 

1192 

282 

1198 

294 

2.4 

4234 

32 

5055 

79 

4.4 

5644 

2 

.5 

1474 

260 

1492 

283 

2.5 

4266 

24 

5134 

68 

4.5 

5646 

2 

.6 

1740 

260 

1775 

283 

2.6 

4290 

20 

5202 

68 

4.6 

5648 

1 

.7 

2000 

234 

2058 

260 

2.7 

4310 

14 

5270 

57 

4.7 

5649 

1 

.8 

2234 

229 

2318 

260 

2.8 

4324 

9 

5327 

45 

4.8 

5650 

1 

.9 

2463 

214 

2578 

249 

2.9 

4333 

7 

5372 

45 

4.9 

5651 

1 

1.0 

2677 

200 

2827 

238 

3.0 

4340 

3 

5417 

34 

5.0 

5652 

6 

1.1 

2877 

186 

3065 

226 

3.1 

4343 

2 

5451 

34 

5.1 

5652.6 

5 

1.2 

3063 

172 

3291 

215 

3.2 

4345 

5485 

23 

5.2 

5653.1 

3 

1.3 

3235 

157 

3506 

204 

3.3 

5508 

23 

5.3 

5653.4 

3 

1.4 

3392 

134 

3710 

181 

3.4 

5531 

23 

5.4 

5653 . 7 

3 

1.5 

3526 

129 

389 1 

181 

3.5 

5534 

23 

5.5 

5654.0 

3 

1.6 

3655 

108 

4072 

158 

3.6 

5577 

11 

5.6 

5654.3 

?. 

1.7 

3763 

103 

4230 

158 

3.7 

5.588 

11 

5.7 

5654.5 

7. 

1.8 

3866 

84 

4388 

136 

3.S 

5599 

11 

5.8 

5654.7 

2 

1.9 

3950 

73 

4524 

124 

3.9 

5610 

11 

5.9 

5654.9 

2 

2.0 

4023 

4648 

4.0 

5621 

6.0 

5655.1 

96         spelling  Ability — Its  Measurement  and  Distribution 


TABLE  XXXIX 

Modified  Table  of  Frequency,  6th  Grade.     Median  =+0.418P.E. 

Plan  of  elimination:  —2.7  P.E.,  100%;  —1.7  P.E.,  60%;  —0.7  P.E., 
35%;  +0.3  P.E.,  15%;  +1.3  P.E.,  10%;  +2.3  P.E.,  5%;  +3.3  P.E., 
0%.    Total  area  of  surface  of  frequency  taken  as  10,000.     See  Fig.  40. 


X 

Low 

High 

X 

Low 

High 

X 

P.E. 

Low 

High 

P.E. 

% 

A 

% 

A 

P.E. 

or 
/c 

A 

% 

A 

% 

A 

% 

A 

•SOI 

309 

44 

145 

7 

.1 

301 

29.3 

309 

312 

2.1 

3602 

31 

5235 

121 

4.1 

6268 

7 

.2 

594 

27.1 

621 

316 

2.2 

3633 

26 

5356 

120 

4.2 

6275 

7 

.3 

869 

268 

937 

316 

2.3 

3659 

16 

5476 

95 

4.3 

6282 

6 

.4 

1137 

261 

1253 

313 

2.4 

3675 

11 

5571 

95 

4.4 

6288 

3 

.5 

1398 

244 

1506 

308 

2.5 

3686 

7 

5666 

82 

4.5 

6291 

3 

.6 

1642 

237 

1874 

305 

2.6 

3693 

3 

5748 

82 

4.6 

6294 

1.4 

.7 

1879 

212 

2179 

284 

2.7 

3696 

5830 

69 

4.7 

6295.4 

1.4 

.8 

2091 

203 

2463 

285 

2.8 

5899 

55 

4.8 

6296  8 

1.4 

.9 

2294 

186 

2748 

275 

2.9 

5951 

55 

4.9 

6298.2 

1.4 

1.0 

2480 

171 

3023 

264 

3.0 

6009 

42 

5.0 

6299.6 

.7 

1.1 

2651 

^r,!^ 

3287 

252 

3.1 

6051 

42 

5.1 

6300.3 

.7 

1.2 

2806 

141 

3539 

241 

3.2 

6093 

28 

5.2 

6301 

.4 

1.3 

2947 

127 

3780 

2.30 

3.3 

6121 

28 

5.3 

6301.4 

.4 

1.4 

3074 

107 

4010 

206 

3.4 

6149 

28 

5.4 

6301.8 

.4 

1.5 

3181 

102 

4216 

206 

3.5 

6177 

28 

5.5 

6302.2 

.4 

1.6 

3283 

85 

4422 

182 

3.6 

6205 

14 

5.6 

6302.6 

.28 

1.7 

3368 

79 

4604 

183 

3.7 

6219 

14 

5.7 

6302.88 

.28 

1.8 

3447 

61 

4787 

158 

3.8 

6233 

14 

5.8 

6303.16 

.23 

1.9 

3508 

50 

4945 

145 

3.9 

6247 

14 

5.9 

6303 . 44 

.28 

2.0 

3558 

5090 

4.0 

6261 

6.0 

6303 . 72 

Derived  Forms  of  Distribution 


97 


TABLE  XL 

Modified  Table  of  Frequency,  7th  Grade.     Median= +0.669  P.E. 

Plan  of  elimination:  —2.3  P.E.,  100%;  —1.3  P.E.,  70%;  —0.3  P.E., 
50%;  +0.7  P.E.,  20%;  +1.7  P.E.,  10%;  +2.7  P.E.,  5%;  +3.7  P.E., 
0%.     Total  area  of  frequency  surface  taken  as  10,000.     See  Fig.  41. 


X 

Low 

High 

X 

P.E. 

Low 

High 

X 

P.E. 

Low 

High 

P.E. 

% 

A 

% 

A 

7o 

A 

% 

A 

% 

A 

% 

A 

277 

290 

17 

176 

9 

.1 

277 

263 

290 

306 

2.1 

2844 

9 

5846 

145 

4.1 

7096 

9 

.2 

540 

240 

596 

308 

2.2 

2853 

5 

5991 

145 

4.2 

7105 

9 

.3 

780 

226 

904 

322 

2.3 

2858 

6136 

114 

4.3 

7114 

7 

.4 

1006 

217 

1226 

334 

2.4 

6250 

114 

4.4 

7121 

3 

.5 

1223 

200 

1560 

336 

2.5 

6364 

99 

4.5 

7124 

3 

.6 

1423 

191 

1896 

348 

2.6 

6463 

99 

4.6 

7127 

2 

.7 

1614 

169 

2244 

326 

2.7 

6562 

83 

4.7 

7129 

2 

.8 

1783 

160 

2570 

326 

2.8 

6645 

66 

4.8 

7131 

2 

.9 

1943 

146 

2890 

318 

2.9 

6711 

68 

4.9 

7133 

2 

1.0 

2089 

132 

3214 

306 

3.0 

6779 

50 

5.0 

7135 

.9 

1.1 

2221 

118 

3520 

296 

3.1 

6829 

50 

5.1 

7135.9 

.9 

1.2 

2339 

106 

3816 

283 

3.2 

6879 

35 

5.2 

7136.8 

.5 

1.3 

2445 

94 

4099 

273 

3.3 

6914 

35 

5.3 

7137.3 

.5 

1.4 

2539 

75 

4372 

246 

3.4 

6949 

35 

5.4 

7137.8 

.5 

1.5 

2614 

66 

4018 

246 

3.5 

6984 

35 

5.5 

7138.3 

.5 

1.6 

2680 

50 

4864 

220 

3.6 

7019 

17 

5.6 

7138.8 

.35 

1.7 

2730 

43 

5084 

220 

3.7 

7036 

17 

5.7 

7139.15 

.35 

1.8 

2773 

31 

5304 

190 

3.8 

7053 

17 

5.8 

7139.50 

.35 

1.9 

2804 

23 

5494 

176 

3.9 

7070 

17 

5.9 

7139.85 

.3 

2.0 

2827 

5670 

4.0 

7087 

6.0 

7140.15 

98         spelling  Ability— Its  Measurement  and  Distribution 


TABLE  XLI 

Modified  Table  of  Frequency,  8th  Grade.     Median= +0.746  P.E. 

Plan  of  elimination:  —2  P.E.,  100%;  —1  P.E.,  70%;  0  P.E.,  50%;  +1 
P.E.,  30%;  +2P.E.,  20%;  +3  P.E.,  10%;  +4  P.E.,  6%;  +5  P.E.,  2%; 
+  6  P.E.,  0%.    Total  area  of  frequency  surface  taken  as  10,000.    See  Fig.  42. 


X 

Low 

High 

X 

P.E. 

Low 

High 

X 

P.E. 

Low 

High 

P.E. 

% 

A 

% 

A 

% 

A 

% 

A 

% 

A 

% 

A 

280 

290 

184 

10 

.1 

280 

270 

290 

303 

2.1 

5834 

165 

4.1 

7195 

10 

.2 

550 

249 

593 

303 

2.2 

5999 

145 

4.2 

7205 

10 

.3 

799 

237 

896 

313 

2.3 

6144 

130 

4.3 

7215 

8 

.4 

1036 

226 

120r 

323 

2.4 

6274 

116 

4.4 

7223 

4 

.5 

1262 

207 

1531i 

323 

2.5 

6390 

108 

4.5 

7227 

4 

.6 

1469 

197 

1855 

.332 

2.6 

6498 

108 

4.6 

7231 

2 

.7 

1666 

172 

2187 

320 

2.7 

6606 

91 

4.7 

7233 

2 

.8 

1838 

162 

2507 

319 

2.8 

6697 

75 

4.8 

7235 

2 

.9 

2000 

145 

2826 

319 

2.9 

6772 

75 

4.9 

7237 

2 

1.0 

2145 

131 

3145 

309 

3.0 

6S47 

56 

5.0 

7239 

1 

1.1 

2276 

112 

3454 

299 

3.1 

6003 

56 

5.1 

7240 

1 

1.2 

2388 

95 

3753 

2SS 

3.2 

69.59 

38 

5.2 

7241 

.6 

1.3 

2483 

79 

4041 

276 

3.3 

6997 

38 

5.3 

7241.6 

.6 

1.4 

2562 

60 

4317 

260 

3.4 

7035 

37 

5.4 

7242.2 

.6 

1.5 

2622 

50 

4577 

242 

3.5 

7072 

37 

5.5 

7242.8 

.6 

1.6 

2672 

35 

4819 

235 

3.6 

7109 

19 

5.6 

7243.4 

.4 

1.7 

2707 

27 

5054 

215 

3.7 

7128 

19 

5.7 

7243.8 

.4 

1.8 

2734 

14 

5269 

197 

3.8 

7147 

19 

5.8 

7244.2 

.4 

1.9 

2748 

6 

5466 

184 

3.9 

7166 

19 

5.9 

7244.6 

.4 

2.0 

2754 

5650 

4.0 

7185 

6.0 

7245 

In  this  manner  each  of  the  Modified  Tables  of  Frequency  was 
made  up.  They  are  given  in  tables  XXXVI  to  XLI.  They 
are  intended  to  take  the  place,  each  for  the  grade  to  which  it 
applies,  of  the  Table  of  Frequency  for  the  normal  distribution. 
Since  they  are  asymmetrical,  the  lower  and  upper  parts  have  to 
be  given  separately.  For  the  same  reason  there  is  no  P.E.,  the 
use  of  the  Probable  Error  as  a  unit  of  amount  being  properly 
confined  to  normal  curves  only  (Yule,  '11,  p.  147).  The 
quartile  deviation    (Qt,  —  Oi)    might  be  used  instead,   but  its 


Derived  Forms  of  Distribution 


99 


A 

^^  W 

/A 

1 

c 

'' 

^ 

V^' 

/A 

^ 

"^^     t^ 

c 

)      r 

T 

\             5"  Gk,t  c*.A.e^. 

Figs.  37-42.     Derived  Forms  of  Distribution.     Grades  3  to  8. 


loo       spelling  Ability — Its  Measurement  and  Distribution 

value  differs  for  each  of  the  six  tables.  In  order  therefore  to 
employ  a  unit  which  should  be  the  same  for  all,  including  the 
normal  distribution,  we  have  retained  the  P.E.  of  the  Proba- 
bility Integral.  It  is  now  no  longer  a  function  of  the  modified  dis- 
tributions, but  a  mere  unit  of  length.  Likewise  in  order  to 
have  a  common  point  of  reference  the  median  of  the  normal 
distribution  has  been  retained,  the  terms  "  low  "  and  "  high  "  in 
the  tables  referring  to  parts  below  or  above  that  point.  The 
real  median  of  each  modified  distribution,  however,  is  given, 
being  expressed  as  a  deviation  from  the  old  median. 

Figs.  37  to  42  are  to  be  considered  in  connection  with  tables 
XXXVI  to  XLI,  of  which  they  are  the  graphic  expressions  (the 
curves  being  "  smoothed,"  to  represent  an  indefinite  number  cf 
cases) .  They  are  also  to  be  considered  in  connection  with  Figs.  31 
to  36,  from  the  "  retention  "  parts  of  which  they  are  derived 
by  making  the  areas  10,000.  In  Figs.  37  to  42,  the  curve  extend- 
ing farther  to  the  left  is  in  each  case  the  normal  curve  and 
OM  is  its  median  vertical.  O^M^  is  the  median  vertical  of  the 
modified  surface  and  00^  is  the  distance  between  medians.  The 
values  of  these  are  as  follows:  3d  grade,  0.051  P.E. ;  4th 
grade,  0.087  P-E. ;  5th  grade,  0.215  P.E. ;  6th  grade,  0.418  P.E. ; 
7th  grade,  0.669  P-E. ;  8th  grade,  0.746  P.E. 

Is  it  worth  while  to  use  these  tables  instead  of  the  normal 
one?  Will  the  same  material  when  analyzed  by  the  skew  and 
normal  distributions  yield  differences  that  are  important?  With 
the  purpose  of  throwing  some  light  on  this  question  we  have 
used  the  modified  tables  to  interpret  the  results  of  testing  with  our 
Preferred  List,  and  the  rest  of  the  present  section  will  be 
devoted  to  this  matter.  The  differences  will  not  in  many  cases 
be  found  to  be  large.  This  is,  of  course,  particularly  true  when 
the  early  grades  are  concerned,  the  curves  being  for  those  grades 
almost  normal.  It  may  be  remarked,  however,  that  the  applica- 
bility of  these  tables  does  not  rest  upon  the  results  here  shown. 
It  is  general  ability  rather  than  spelling  ability  that  tends 
strongly  to  keep  children  in  school.  Spelling  ability  does  not 
correlate  as  highly  with  general  ability  as  do  the  abilities 
in  most  other  school  subjects.     It  is  quite  likely,  therefore,  that 


Derived  Forms  of  Distribution 


lOI 


the  use  of  these  tables  for  the  statistical  treatment  of  other 
subjects  may  be  more  satisfactory  than  it  is  for  spelling.  They 
are  given  here  primarily  to  illustrate  the  method. 

TABLE  XLII 

Number  and  Per  Cent  of  Pupils  in  Each  Grade  Whose  Ability 
Equalled  or  Exceeded  that  of  the  Median  Pupil  in  Evert  Other  Grade 
WITH  the  P.E.  Values  Corresponding  to  Each  Per  Cent.  Selected 
List.    Modified  Distributions.     Compare  with  Table  XV  (p.  36) 


3(1 

4th 

5th 

6th 

7th 

8th 

Grade 

Grade 

Grade 

Grade 

Grade 

Grade 

3d  grade. . . 

No. 

76 

27 

9 

3 

0 

iV— 445 

% 

17.1 

6.1 

2.0 

0.7 

0 

P.E. 

1 . 3858 

2.2736 

3.0029 

3.607 

? 

4th  grade.  . 

No. 

378 

146 

52 

27 

9 

iV=467 

% 

80.9 

31.3 

11.1 

5.8 

1.9 

P.E. 

1 . 1949 

.6965 

1.7616 

2.2778 

3.0076 

5th  grade.  . 

No. 

478 

370 

142 

73 

30 

A^=515 

% 

92.8 

71.8 

27.6 

14.2 

5.8 

P.E. 

1.7916 

.7341 

.8136 

1 . 5172 

2.2104 

6th  grade. . 

No. 

414 

384 

338 

142 

57 

A^=418 

% 

99.0 

91.9 

80.1 

34.0 

13.6 

P.E. 

2.5043 

1.6747 

1.0451 

.5386 

1.4812 

7th  grade . . 

No. 

363 

354 

328 

256 

99 

iV=365 

% 

99.5 

96.4 

89.9 

70.1 

27.1 

P.E. 

2.6038 

2.0360 

1 . 5096 

.6586 

.7564 

8th  grade .  . 

No. 

227 

276 

269 

241 

200 

N=277 

% 

100 

99.6 

97.1 

87.0 

72.2 

P.E. 

? 

2.4719 

2.0197 

1 . 4424 

.635 

In  Section  ii  we  located  the  grade  medians  assuming  normal 
distribution.  In  Tables  XLII  and  XLIII  the  same  data  have 
been  subjected  to  analysis  using  the  modified  distributions. 
These  tables  are  to  be  compared  with  Tables  XV  (page  36)  and 
XVI  (page  39).  The  median  intervals  are  considerably  less 
than  they  were  found  to  be  by  using  the  normal  distribution. 
Note  the  comparisons  in  Table  XLIV  (page  103). 

On  the  average,  the  intervals  by  the  present  method  are  less 
than  the  same  intervals  found  by  using  the  normal  distribution 
by  0.1247  P.E.,  or  about  half  a  step  in  the  lo-point  scale  (Table 
XX,  page  52).     Since  this  occurs  five  times  the  entire  range 


10  2       Spelling  Ability — Its  Measurement  and  Distribution 


TABLE  XLIII 

Direct  and  Derived  Values  of  Median  Distances.     Modified  Distribu- 
tions.    Selected  List 


Ms-, 

^4-5 

^^5-6 

^8-7 

^7-8 

1 . 3858 
(direct) 

.8878 
(^3-5-^3-4) 

.7293 

.6041 

(M3_,-M3_,) 

? 

(M3_8— Mg.^) 

1.5771 

.6965 
(direct) 

1.0651 

(^4-6-^^5) 

.5162 

.7298 

1.2413 

.9478 

.8136 
(direct) 

.7036 
(M,_-M5_«) 

.6932 

1.3292 

.7606 

.9786 
(^5-7-^6-7) 

.5386 
(direct) 

.9426 

(Me_8-M_,) 

{M,_~M,_,) 

.7972 

.7292 

.7248 

.7564 
(direct) 

1 . 1949 

(direct) 

.5967 
(^5-3-^4-3) 

.7127 

(M,_3-M,_3) 

.0995 
(M,_3-M_3) 

iM,_,-M,_,) 

1.0575 

(^5-3-^5-.) 

.7341 
(direct) 

.9406 
(^6-4-^^4) 

.3613 

.4359 

(M8_,-M,_,) 

.8296 

.9406 
iM,_,-M,_,) 

1.0451 

(direct) 

.4645 

.5101 

.5678 

(M,_3-M,_,) 

.5264 
(^7-4-^7-5) 

.8510 

.5386 
(direct) 

.7838 

(M8_g-M,_„) 

? 

.4522 

.5773 

.8074 

.6350 
(direct) 

Average. . 

1.1479 

.7340 

.8443 

.5359 

.6858 

Weighted 
Average 

1.2008 

.7483 

.8685 

.5606 

.7065 

from  Ms  to  M^  is  contracted  by  0.7235  P.E.,  an  amount  which 
is  more  than  some  grade  intervals  (Mg.^  by  normal  dis.,  M^.^ 
and  M^-g  by  modified  dis.).  This  is  an  important  difiference. 
In  the  matter  of  scaling  the  words,  there  is,  as  might  be 
supposed,  very  little  difference  for  the  3d  grade — so  little  as 
to  be  quite  negligible.  For  the  4th  grade  there  is  some  difference, 
and   for  each  successive  higher  grade  the   difference  between 


Derived  Forms  of  Distribution 


103 


the  placings  of  the  same  word  by  the  two  methods  becomes 
greater  and  greater  as  the  asymmetry  of  the  modified  curves 
becomes  more  and  more  pronounced. 


TABLE  XLIV 

Comparison  of  Averages  of  Median  Distances  by  Normal  Distribu- 
tion AND  BY  Modified  Distributions 


Normal  Distribution 


Modified  Distributions 


Unweighted 
Averages 

Weighted 
Averages 

Unweighted 
Averages 

Weighted 
Averages 

M^  ^ 

1.3326 
0.8471 
1.0406 
0.6344 
0.9201 

1 .  3505 
0.8363 
1.0505 
0.6608 
0.9101 

1 . 1479 
0.7340 
0.8443 
0.5359 
0.6858 

1 . 2008 

,  ,3-4 

M.  „ 

0 . 7483 

M-_- 

0.8685 

Mt 

0.5606 

Mr 

0.7065 

Table  XLV  compares  the  deviations  from  grade  medians  of 
the  words  of  the  Preferred  List  by  Normal  Distribution  and 
by  Modified  Distributions.  Figs.  43  to  47  give  the  same  facts 
in  graphic  form.  Words  spelled  by  50  per  cent  of  pupils  are 
of  course  always  at  o.  Words  spelled  by  more  than  50  per  cent 
of  pupils  do  not  deviate  from  the  median  as  much  by  modified 
as  by  normal  distribution.  The  same  is  true  of  those  spelled  by 
less  than  50  per  cent  of  pupils.  The  easier  a  word  is  and  the 
harder  a  word  is,  the  greater,  accordingly,  is  the  difiference  in 
placing.  The  effect  therefore  of  the  modified  distributions  is  to 
shorten  the  range  of  the  grade  scales.  In  using  the  scales, 
especially  for  pupils  of  the  higher  grades,  all  differences  in 
ability  between  individuals  or  groups  would  tend  to  be  decreased. 
It  seems  likely  that  these  differences  are  in  reality  more  nearly 
what  the  modified  distributions  show  them  to  be.  The  wide 
range  of  the  normal  curve  especially  when  its  spread  is  assumed 
to  be  the  same  for  all  grades  would  seem  to  extend  too  far, 
particularly  towards  the  low  end.  On  the  other  hand,  it  should 
be  said  that  for  the  words  used  in  our  scale  the  normal  distribu- 
tion gives  results  that  are,  practically  speaking,  satisfactory  for 
grade  scales. 


I04       Spelling  Ability — Its  Measurement  and  Distribution 


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io6       Spelling  Ability — Its  Measiirer.ieni  and  Distribution 


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io8       Spelling  Ability — Its  Measurement  and  Distribution 

Table  XLVI  and  Fig.  48  show  a  comparison  for  all  grades 
combined.  The  same  shortening  of  the  range  is  evident  but, 
whereas  the  contraction  in  the  grade  scales  was  more  pro- 
nounced at  the  low  ends,  it  is  now  in  the  general  scale  more 

TABLE  XLVI 
The  Average  Position  of  Each  Word  According  to  Normal  Distribu- 
tion AND  According  to  Modified  Distribution.     Point  of 
Reference  is  3d  Grade  Median.     See  Fig.  48 


Word 

Average  Position 

Word 
No. 

Word 

Average  Position 

Word 
No. 

Nor- 
mal 
Distri- 
bution 

Modi- 
fied 
Distri- 
bution 

Nor- 
mal 
Distri- 
bution 

Modi- 
fied 
Distri- 
bution 

1 
2 
3 
4 
5 

6 

7 

8 

9 

10 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

even 

lesson 

only 

smoke 

front 

sure 

pear 

bought 

another .... 
forty 

pretty 

wear 

button 

minute 

cousin 

nails 

janitor 

saucer 

stopping .  .  . 
sword 

freeze 

touch 

whistle 

carriage.  .  .  . 
nor 

.699 

1.135 
.569 
.835 

1.057 

1.568 
1.958 
1.169 
1.078 
1.758 

1.311 

1.844 
2.026 
1,943 
1.681 

1.379 
2.047 
2.604 
2.213 
2.185 

1.740 

1 .  709 

2 .  193 
2.340 
1.652 

.753 
1.018 
.604 
.831 
.949 

1.349 
1.697 
1.057 

1.287 
1.477 

1.137 
1.587 
1.724 
1.687 
1.491 

1 .  226 
1.773 
2.256 
1.894 
1.766 

1.517 
1 .  465 
1.870 
2.022 
1 .  397 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

already 

beginning. . . 
chicken .... 

choose 

circus 

grease 

pigeons 

quarrel 

saucy  

tailor 

telegram .... 
telephone. . . 
tobacco  .... 

too 

towel 

Tuesday 

tying 

whole 

against 

answer 

butcher. .  . . 

guess 

instead 

raise  

beautiful  .  . . 

2.699 
2.917 
.897 
2.502 
2.141 

3.294 
2.739 
2.069 
2.666 
1.866 

2.549 
2.413 
1.988 
3.491 
1.978 

1.550 
1.870 
2.018 
2.106 
1.594 

1.473 
2 .  363 
1 .  756 
1 .  652 
1.682 

2.305 
2.525 
.872 
2.143 
1.872 

2.838 
2.378 
1.816 
2.294 
1.579 

2.204 
2.101 
1.767 
2.998 
1.718 

1.313 
1.578 
1.751 
1.847 
1.425 

1.308 
2,038 
1.517 
1.456 
1.519 

evident  at  the  high  end.  There  are  also  differences  in  arrange- 
ment, as  there  could  not  be  in  the  grade  scales.  If  two  words 
which  take  the  same  position  on  the  normal  scale  by  ratings 
markedly  different  in  upper  and  lower  grades,  but  balancing 
each  other  in  the  aggregate,  these  words  would  not  take  the 
same   position    on    the   modified    scale.      The   one    which    had 


Derived  Forms  of  Distribution 


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spelling  Ability — Its  Measurement  and  Distribution 


relatively  low  ratings  in  the  lower  grades  would  take  a  position 
above  the  other  whose  ratings  were  relatively  high  in  the  lower 
grades.  This  is  because  the  modified  distributions  in  the  upper 
grades  are  such  that  counting  in  from  the  high  end  more  rapidly 
approaches  the  median  than  does  counting  in  the  same  per  cent 
of  the  area  of  the  normal  curve.  Take  for  example  the  words 
25  nor  and  45  ansiver.  Compare  the  per  cent  ratings  in  Table 
XLV.  Nor  is  easy  in  low  grades  and  hard  in  upper  grades, 
relative  to  answer.  With  the  same  normal  distribution  for  all 
grades  nor  is  a  little  harder  than  anszver.  By  the  modified  dis- 
tributions it  is  easier.  Other  words  may  easily  be  selected  in 
Fig.  48  which  show  differences  in  arrangement.  It  is  therefore 
true  that  the  use  of  modified  forms  of  distribution  makes  a 
difference  which  is  worth  noting  in  the  scaling  of  words.  A 
question  to  be  decided  on  the  evidence  of  more  complete  testing 
and  a  wide  use  of  these  forms  of  distribution  is  whether  the 
differences  here  shown  to  exist  impair  the  usefulness  of  the 
scales  we  have  previously  derived.  Our  judgment  at  present 
is  that  they  do  not. 

§  20.     Conclusions 

We  have  now  certain  data  in  hand  and  we  may  make  a  few 
general   statements   from  them. 

We  have  selected  from  a  school  list  of  about  5000  words  a 
list  for  test  purposes  in  grades  3-8  which,  when  put  in  sentences, 
yielded  a  list  of  270  words.  As  a  result  of  testing  in  two  schools 
a  selected  list  of  100  words  was  chosen  and  to  it  were  added, 
at  a  later  time,  18  more.  These  were  dictated  at  three  schools 
and  the  100  words  alone  subsequently  at  two  more  schools. 
From  the  118  were  chosen  two  lists  of  25  each.  The  three 
successive  selections  were  made  with  the  purpose  of  securing 
words  which  were  easy  enough  in  the  3d  grade  and  hard  enougii 
in  the  8th  grade  to  afford  a  test  in  those  and  therefore  in  inter- 
mediate grades,  and  which  showed  regular  increases  in  per  cent 
correct  from  grade  to  grade.  The  two  25-word  lists  were  then 
subjected  to  analysis  and  found  to  have  high  correlations 
between  grades  and  between  schools. 

Using  the  entire  test  material  and  the  ratings  of  individual 
pupils  and  assuming  normal  distribution  and  equal  variability, 


Conclusion  1 1 1 

the  differences  between  typical  grade  abilities  were  found  and 
expressed  as  median  intervals. 

The  50  words  which  had  been  derived  by  a  threefold  selective 
process  and  subjected  to  close  inspection  for  permanency  as 
between  grades  and  schools  were  scaled  for  each  grade  and  for 
all  grades  combined.  By  using  an  "  Easy  50- Word  List "  an 
expression  was  derived  for  the  zero-point;  and,  by  further  test- 
ing under  rigidly  controlled  conditions,  previous  grade-intervals 
were  verified. 

To  fill  in  and  extend  the  scale,  the  Rice  Sentence  Test  was 
dictated  and  the  word-scores  for  the  Easy  50-Word  List  were 
used.  It  is  to  be  understood,  however,  that  neither  of  these  lists 
was  subjected  to  the  scrutiny  that  was  made  of  the  Preferred 
List.  Accordingly  we  cannot  regard  the  placing  of  these  words 
as  very  reliable. 

Finally  we  have  derived  and  applied  tables  of  frequency 
more  or  less  asymmetrical  in  character  according  to  the  amount 
of  retention  for  each  grade  and  its  estimated  distribution.  By 
using  them,  results  have  been  obtained  which  in  some  instances 
differ  considerably  from  those  obtained  on  the  basis  of  a  normal 
distribution.  Such  differences  as  appear  are,  we  are  convinced, 
differences  in  the  direction  of  a  truer  representation  of  the  facts. 
On  the  whole,  however,  the  differences  are  not  sufficient  to 
impair  our  previous  results  for  any  practical  use  which  is  likely 
to  be  made  of  them. 

It  has  become  evident  to  us  that  there  is  a  lack  of  knowledge 
of  the  spelling  problem  not  only  among  teachers  but  also  among 
those  who  direct  their  work.  This  is  unfortunate,  considering 
the  relative  definiteness  of  the  subject  and  the  comparative  ease 
with  which  results  in  it  may  be  scored.  Nor  is  there  any  special 
consciousness  of  the  need  of  more  insight  in  this  matter.  Almost, 
if  not  quite,  all  the  studies  that  have  hitherto  been  made  have 
dealt  with  individual  performances.  The  behavior  of  words  has 
received  no  attention. 

It  is  our  belief,  however,  that  a  powerful  improvement  in  the 
teaching  of  spelling  may  be  derived  from  a  more  critical  knowl- 
edge and  more  accurate  judgment  on  the  part  of  teachers  and 
supervisors  of  the  material  of  the  subject — i.e.,  of  the  words  of 
the  language.  If  in  a  list  of  50  words  the  one  word  that  is 
incontestably  hardest  is  by  more  than  one-fourth  of  a  rcpresenta- 


112       Spelling  Ability — Its  Measurement  and  Distribution 

tive  group  of  teachers  judged  to  be  the  easiest,  or  the  easiest 
but  one,  that  fact  in  itself  is  a  very  good  reason  why  the  word 
is  so  hard.  Pupils  misspell  it  because  their  teachers  do  not 
realize  the  need  of  teaching  it.  If  text-book  makers  disagree 
so  widely  as  to  put  the  same  words  in  grades  that  are  three, 
four,  and  even  five  years  apart,  it  is  proof  of  the  confusion  that 
exists  as  to  how  hard  words  are,  and  when  they  should  be 
taught.  There  are  various  types  of  words,  and  each  type 
requires  different  treatment.  There  is  the  type  that  does  not 
need  to  be  taught  at  all.  There  is  the  type  which  appears  easy  in 
the  lower  classes  and  (grade  considered)  hard  in  the  upper 
classes.  Such  may  have  been  prematurely  taught  in  the  lower 
classes.  There  is  the  type  that  appears  to  possess  special  difficulty 
for  the  middle  grades.  This  is  due  to  a  constant  cause — e.g.,  in 
the  case  of  ivhosc,  to  the  learning  of  the  use  of  the  apostrophe 
in  possessives.  There  are  types  of  errors ;  there  is  the  problei,i 
of  substitution,  of  illegibility,  and  of  omission. 

To  obtain  any  accurate  notion  of  "  word  behavior  "  we  must 
rate  for  words  as  distinct  from  individuals.  Moreover  we  must 
give  our  per  cent  ratings  thus  obtained  an  interpretation  for 
difficulty  which  takes  account  of  the  distribution  of  spelling 
ability.  When  we  do  so  we  shall  find  how  unreliable  percentages 
are  as  indicating  differences  in  difficulty.  We  shall  find,  for 
instance,  that  a  difference  of  lo  per  cent  between  two  words 
rated  89  and  99  means  more  than  four  times  as  great  a  dift'erence 
in  difficulty  as  is  that  between  two  words  rated  at  45  and  55, 
although  the  percentage  difference  is  in  both  cases  the  same. 
Table  XLVII  (See  appendix)  is  a  ready  reckoner  for  the  con- 
version of  percentages  into  units  that  take  account  of  the  form 
of  distribution,  assuming  it  to  be  '  Normal.' 

If  this  study  does  no  more  than  show  the  need  of  word 
criticism  and  indicate  a  method,  it  may  be  worth  while.  Every 
school  affords  a  place  and  every  day  a  time  at  which  something 
may  be  done  to  help  throw  light  on  the  nature  of  the  material 
we  deal  with  in  spelling.  All  such  work  should  be  collected  and 
made  generally  available.  If  teachers,  principals,  or  superin- 
tendents who  have  made  or  who  hereafter  make  a  study  of  the 
difficulty  of  words,  will  submit  them  to  the  author  of  this  study, 
the  data  will  be  gratefully  received  and  utilized  to  disseminate 
a  larger  and  more  accurate  knowledge. 


APPENDIX 

I.     List  of  Authors  axd  Titles  Specifically  Referred  to 

IN  the  Text 

TiiORNDiKE,   E.   L.    ('lo).    Handwriting.     Teachers  College  Record,  Vol. 

XI,  No.  2. 
HiLLEGAS,  MiLO  B.   ('12).     A  Scalc  for  the  Measurement  of  Quality  in 

English     Composition     by     Young     People.       Teachers    College 

Record,  Vol.  XIII,  No.  4. 
Rice,  J.   M.    ('97).     The   Futility  of   the   Spelling   Grind.     Forum,  Vol. 

XXIII,  pp.  163-172;  409-419. 
Thorndike,  E.  L.   ('13).     An  Introduction  to  the  Theory  of  Mental  and 

Social  Measurements.     Second  Edition.     Teachers  College,  New 

York. 
CoRNMAN,  O.   P.    ('02).     Spelling  in  the  Elementary   School.     Ginn   and 

Co.,    New    York. 
Wallin,  J.  E.  Wallace,    ('ii).     Spelling  Efficiency  in  Relation  to  Age, 

Grade,  and   Sex,  and  the  Question  of  Transfer.     Warwick  and 

York,  Baltimore. 
Pearson,    Henry    C.    ('12).     Experimental    Studies   in   the   Teaching  of 

Spelling.     Teachers  College  Record,  Vol.  XIII,  No.  i. 
Spearman,    C.     ('06).      'Foot-rule'    for    Measuring    Correlation.      Brit. 

Journ.   of  Psych.,  Vol.   II,  Pt.   I,  July,    1906. 
Brown,  William,   ('ii).     The  Essentials  of  Mental  Measurement.     Put- 
nam, New  York. 
Whipple,  Guy  Montrose.   ('10).     Manual  of  Mental  and  Physical  Tests. 

Warwick  and  York,  Baltimore. 
Klein,  Linus  W.  ('12).     A  Study  in  the  Psychology  of  Spelling.    Journ. 

of  Ed.  Psych.,  Vol.   Ill,   No.  7- 
Thorndike,    E.    L.    ('07).      The    Elimination    of    Pupils    from    School. 

Bureau  of  Education,  Bulletin  No.  4,  1907. 
Ayres,    Leonard    P.    ('09).      Laggards    in    our    Schools.      Russell    Sage 

Foundation,  New  York. 
Thorndike,    E.    L.     ('10).      Promotion,    Retardation,    and    Elimination. 

Psych.  Clinic,  Vol.  HI,  No.  8  and  9. 
Str.\yer,  George  Drayton  ('ii).    Age  and  Grade  Census  of  Schools  and 

Colleges.     Bureau  of  Education,   Bulletin   No.  5,   191 1. 
Yule,    G.   Udney    ('ii).     An    Introduction   to   the   Theory  of   Statistics. 

Lippincott,    Philadelphia. 


114      Spelling  Ability — Its  Measurement  and  Distribution 


II.    Lists  Referred  to  in  the  Text  and  Used  in  the  Scales 


44.  deceive 

45.  driving 

46.  surface 

47.  rough 

48.  smooth 

49.  hopping 

50.  certainly 

51.  grateful 

52.  elegant 

53.  present 

54.  patience 

55.  succeed 

56.  severe 
K-7.  accident 

58.  sometimes 

59.  sensible 

60.  business 

61.  answer 

62.  sweeping 

63.  properly 

64.  improvement 

65.  fatiguing 

66.  anxious 

67.  appreciate 

68.  assure 

69.  imagine 

70.  peculiar 

71.  character 

72.  guarantee 

73.  approval 

74.  intelligent 
7g.  experience 

76.  delicious 

77.  realize 

78.  importance 

79.  occasion 

80.  exceptions 

81.  thoroughly 

82.  conscientious 

83.  therefore 

84.  ascending 

85.  praise 

86.  wholesome 


Preferred   List 

Easy   50- Word 

First 

List 

Rice  S 

I. 

even 

I. 

you 

I. 

running 

2. 

lesson 

2. 

will 

2. 

slipped 

3- 

only 

3- 

hear 

3- 

listened 

4- 

smoke 

4- 

him 

4- 

queer 

5. 

front 

5- 

coming 

5- 

speech 

6. 

sure 

6. 

he 

6. 

believe 

7- 

pear 

7- 

is 

7- 

weather 

8. 

bought 

£. 

on 

8. 

changeable 

9- 

another 

C;. 

the 

9- 

whistling 

10. 

forty 

10. 

road 

10. 

frightened 

II. 

pretty 

II. 

and 

II. 

always 

12. 

wear 

12. 

almost 

12. 

changing 

13- 

button 

13. 

sure 

13- 

chain 

14. 

minute 

14. 

to 

14. 

loose 

15- 

cousin 

•  15- 

pass 

15- 

baking 

16. 

nails 

K. 

in 

16. 

piece 

17- 

janitor 

17. 

front 

17- 

receive 

18. 

saucer 

18. 

of 

18. 

laughter 

19. 

stopping 

19. 

me 

19. 

distance 

20. 

sword 

20. 

I 

20. 

choose 

21. 

freeze 

21. 

send 

21. 

strange 

22. 

touch 

22. 

for 

22. 

picture 

23- 

whistle 

23- 

every 

23. 

because 

24. 

carriage 

24. 

day 

24. 

thought 

25 

nor 

25- 

go 

25. 

purpose 

26. 

into 

26. 

learn 

Second 

27. 

school 

27. 

lose 

26. 

already 

28. 

but 

28. 

almanac 

27. 

beginning 

29. 

do 

29. 

neighbor 

28. 

chicken 

30. 

not 

30. 

writing 

29. 

choose 

31. 

touch 

31. 

language 

30. 

circus 

32. 

table 

32. 

careful 

31- 

grease 

33- 

also 

33. 

enough 

32. 

pigeons 

34. 

has 

34- 

necessary 

33- 

quarrel 

35- 

only 

35- 

waiting 

34- 

saucy 

36. 

one 

36. 

disappoint 

35- 

tailor 

37- 

pair 

37- 

often 

36. 

telegram 

38. 

shoes 

38. 

covered 

37. 

telephone 

39- 

they 

39- 

mixture 

38. 

tobacco 

40. 

are 

40. 

getting 

39- 

too 

41. 

at 

41. 

better 

40. 

towel 

42. 

all 

42. 

feather 

41. 

Tuesday 

43- 

pretty 

43- 

light 

42. 

tying 

44. 

no 

43- 

whole 

45- 

man 

44- 

against 

46. 

ought 

45- 

answer 

47- 

steal 

46. 

butcher 

48. 

even 

47- 

guess 

49. 

a 

48. 

instead 

50. 

penny 

49. 

raise 

SO. 

beautiful 

Appendix  115 

III.     Memorandum    on    the    Method   of   Computing   with 
Modified  Frequency  Tables.     (Tables  XXXVI-XLI.) 

1.  Derivation  of  Median  Intervals.  Table  XLII,  lines  4  and  5,  gives 
for  the  4ih  grade  the  number  and  per  cent  of  pupils  who  equal  or  exceed 
the  median  pupil  of  each  of  the  other  grades.  In  line  6  the  correspond- 
ing P.E.  values  are  shown.  These  are  obtained  by  using  Table  XXXVII 
as  follows:  (a)  Since  80.9%  of  4th-grade  pupils  surpass  the  median 
3d-grade  pupil,  deduct  8090  cases  from  the  high  end  of  the  4th-grade 
distribution.  Since  there  are  5236.32  above  M4(nor.  dis.).  2853.68  more 
must  be  taken,  extending  to  a  point  which  is  1.1079  P.E.  below  il/4(nor.  dis.). 
But  hUinoT.  dis.)  is  itself  .087  P.E.  below  MiCmod.  dis.).  Correcting  for  this, 
we  have  1.1949  P.E.  below  M4(mod.  dis.).  ( — 1.1079 — .087  =  —  1.1949.) 
This  is  the  first  entry  in  line  6  of  Table  XLII.  (b)  Deduct  3130  from 
5236.32,  leaving  2106.32.  By  interpellation  this  corresponds  to  +.7835  P.E. 
Subtracting  .0S7  P.E.  as  before,  we  have  -I-.6965,  the  second  entry  in  Hne 
6  of  Table  XLII.  (c)  5236.32  less  mo  gives  4126.32,  corresponding  to 
-f  1.8486  P.E.  Again  subtracting  .087  P.E.,  we  have  +  1.7616  P.E.,  which 
is  the  third  entry  in  line  6,  Table  XLII. 

2.  Scaling  the  Words.  For  "  even,"  Table  XLV.  columns  headed 
"  Modified  Distributions,"  the  figures  are  derived  as  follows,  using  for 
each  grade  its  proper  frequency  table :  Third  Grade.  59%  correct. 
Count  out  the  5900  highest  cases.  There  are  5 141. 7  above  il/aCnor.  dis.). 
We  must,  therefore,  take  758.3  cases  below  that  point.  This  brings  us 
to  — .276  P.E.  Subtracting  (algebraically)  .051  P.E.,  in  order  to  refer 
this  to  MsCmod.  dis.),  we  have  — .327  P.E.,  as  in  Table  XLV.  Fourth 
Grade.  79%  correct.  Counting  out  7900  cases  from  the  high  end,  we  take 
all  the  "highs"  and  2663.32  of  the  "lows,"  reaching  as  far  as  — 1.0212 
P.E.  But  ilfiCmod.  dis.)  is  .087  P.E.  above  MiCnor.  dis.).  Subtracting  this 
amount,  we  have  —  1.108  P.E.  as  in  Table  XLV.  Fifth  Grade.  \Vhen 
percentages  are  high,  it  is  generally  easier  to  count  out  their  complements 
from  the  low  end.  "  Even  "  is  in  this  grade  89%  correct.  We  may  there- 
fore count  8900  cases  from  the  high  end  or  iioo  from  the  losv  end.  In 
either  case  we  reach  the  3245th  case  of  the  "  lows,"  which  corresponds 
to  —  1.306  P.E.  Correcting  for  the  deflection  of  the  median  from  its 
"normal"  position  (.215  P.E.),  we  have  — 1,521  P.E.  as  given.  Sixth 
Grade.  3696  —  700  =  2996.  The  2996th  case  corresponds  to  —  1.339  P.E. 
Median  displacement  =  .418  P.E.  Subtracting  from  — 1.339  P-E.,  we 
have  —  1-757  P-E.,  as  given.  The  7th  and  8th  grade  positions  are  derived 
in  the  same  way,  care  being  taken  to  use  the  proper  grade  table  of  fre- 
quency in  each  case. 

Table  XLVI.  The  average  position  for  each  word  as  given  in  the 
column  headed  "  Modified  Distributions  "  w^as  computed  as  follows :  Add 
to  the  P.E.  value  of  "  even  "  for  each  grade  (Table  XLV)  the  distance 
which  the  grade  median  is  above  the  3rd-grade  median.  From  Table 
XLII  these  distances  are  shown  to  be:  M^-i,  1.148  P.  E. :  M?.-,,  1.882  P.E. ; 
Ms-e,  2.726  P.E. ;  XL--,.  3.262  P.E. ;  il/s-s.  3.948  P.E.  Adding  these  values 
to  those  of  Table  XLV,  beginning  with  the  4th  grade  and  writing  the 
3rd  grade  as  given,  we  have  the  following  P.E.  values :  — .327,  +.040, 
+.361,  -(--969,  +  1. 541,  and  -f  1.932.  The  average  of  these  is  +.753  P.E., 
as  given  for  the  word  "  even  "  in  Table  XLVI.  The  average  positions  of 
the  remaining  words  were  computed  in  the  same  way. 


ii6  Appendix 

IV.  TABLE  XLVII — P.E.  Values  Corresponding  to  Given  Per  Cents 
OF  THE  Normal  Surface  of  Frequency,  Per  Cents  Being  Taken 
from  the  Median 


0 

.1 

2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

0 

.000 

.004 

.007 

.011 

.015 

.019 

.022 

.026 

.030 

.033 

1 

.037 

.041 

.044 

.048 

.052 

.056 

.059 

.063 

.067 

.071 

2 

.074 

.078 

.082 

.085 

.089 

.093 

.097 

.100 

.104 

.108 

3 

.112 

.115 

.119 

.123 

.127 

.130 

.134 

.138 

.141 

.145 

4 

.149 

.153 

.156 

.160 

.164 

.168 

.172 

.175 

.179 

.183 

5 

.187 

.190 

.194 

.198 

.201 

.205 

.209 

.213 

.216 

.220 

6 

.224 

.228 

.231 

.235 

.239 

.243 

.246 

.250 

.254 

.258 

7 

.261 

.265 

.269 

.273 

.277 

.280 

.284 

.288 

.292 

.296 

8 

.299 

.303 

.307 

.311 

.315 

.318 

.322 

.326 

.3.30 

.334 

9 

.337 

.341 

.345 

.349 

.353 

.357 

.360 

.364 

.368 

.372 

10 

.376 

.380 

.383 

.387 

.391 

.395 

.399 

.403 

.407 

.410 

11 

.414 

.418 

.422 

.426 

.430 

.434 

.437 

.441 

.445 

.449 

12 

.453 

.457 

.461 

.464 

.468 

.472 

.476 

.480 

.484 

.489 

13 

.492 

.496 

.500 

.504 

.508 

.512 

.516 

.519 

.523 

.527 

14 

.531 

.535 

.539 

.543 

.547. 

551 

.555 

.559 

.563 

.567 

15 

.571 

.575 

.579 

.583 

.588 

.592 

.596 

.600 

.603 

.608 

16 

.612 

.616 

.620 

.624 

.628 

.632 

.636 

.640 

.644 

.648 

17 

.652 

.656 

.660 

.665 

.669 

.673 

.677 

.681 

.685 

.689 

18 

.693 

.698 

.702 

.706 

.710 

.714 

.719 

.723 

.727 

.731 

19 

.735 

.740 

.744 

.748 

.752 

.756 

.761 

.765 

.769 

.773 

20 

.778 

.782 

.786 

.790 

.795 

.799 

.803 

.807 

.812 

.816 

21 

.820 

.825 

.829 

.834 

.838 

.842 

.847 

.851 

.855 

.860 

22 

.864 

.869 

.873 

.878 

.882 

.886 

.891 

.895 

.900 

.904 

23 

.909 

.913 

.918 

.922 

.927 

.931 

.936 

.940 

.945 

.949 

24 

.954 

.958 

.963 

.968 

.972 

.977 

.982 

.986 

.991 

.996 

25 

1.000 

1.005 

1.009 

1.014 

1.019 

1.024 

1.028 

1.033 

1.038 

1.042 

26 

1.047 

1.052 

1.057 

1.062 

1.067 

1.071 

1.076 

1.081 

1.086 

1.091 

27 

1.096 

1.101 

1.105 

1.110 

1.115 

1.120 

1.125 

1.130 

1.135 

1.140 

28 

1.145 

1.150 

1.155 

1.160 

1.165 

1.170 

1.176 

1.181 

1.186 

1.191 

29 

1.196 

1.201 

1.206 

1.211 

1.217 

1.222 

1.227 

1.232 

1.238 

1.243 

30 

1.248 

1.253 

1.259 

1.264 

1.269 

1.275 

1.279 

1.286 

1.291 

1.296 

31 

1.302 

1.307 

1.313 

1.318 

1.324 

1.329 

1.335 

1.340 

1.346 

1.351 

32 

1.357 

1.363 

1.368 

1.374 

1.380 

1.386 

1.391 

1.397 

1.403 

1.409 

33 

1.415 

1.421 

1.427 

1.432 

1.438 

1.444 

1.450 

1.456 

1.462 

1.469 

34 

1.475 

1.481 

1.487 

1.493 

1.499 

1.506 

1.512 

1.518 

1.524 

1.531 

35 

1.537 

1.543 

1.549 

1.556 

1.563 

1.569 

1.576 

1.582 

1.589 

1.595 

36 

1.602 

1.609 

1.616 

1.622 

1.629 

1.636 

1.643 

1.649 

1.656 

1.663 

37 

1.670 

1.677 

1.685 

1.692 

1.699 

1.706 

1.713 

1.720 

1.728 

1.735 

38 

1.742 

1.749 

1.757 

1.765 

1.772 

1.780 

1.788 

1.795 

1.803 

1.811 

39 

1.819 

1.827 

1.835 

1.843 

1.851 

1.859 

1.867 

1.875 

1.884 

1.892 

40 

1.900 

1.909 

1.918 

1.926 

1.935 

1.944 

1.953 

1.962 

1.971 

1.979 

41 

1.988 

1.997 

2.007 

2.016 

2.026 

2.035 

2.044 

2.054 

2.064  2.074 

42 

2.083 

2.093 

2.103 

2.114 

2.124 

2 .  134 

2.145 

2.155 

2.166 

2.177 

43 

2.188 

2.199 

2.211 

2.222 

2.234 

2.245 

2.257 

2.269 

2.281 

2.293 

44 

2.305 

2.318 

2.331 

2.344 

2.357 

2.370 

2.384 

2.397 

2.411 

2.425 

45 

2.439 

2.453 

2.468  2.483 

2.498 

2.514 

2.530 

2.546 

2.562 

2.579 

46 

2.597  2.614 

2.631 

2.648 

2.067 

2.6S6 

2.706 

2.726 

2.746 

2.767 

47 

2.789 

2.811 

2 .  834 

2.857 

2.881 

2.905 

2.932 

2.958 

2. 986 

3.015 

48 

3.044 

3.077 

3.111 

3.146 

3.182 

3.219 

3. 258 

3.300  3.346  3.395 

49 
50 

3.450 

3.506 

3.571 

3.643 

3.725 

3.820 

3.938 

4.083 

4.275 

4.600 

